Gap-05-catastrophe — Cosmological-constant fine-tuning catastrophe (dissolution): the gate anchor ledger

The honest one-line: the cosmological-constant catastrophe — the demand to cancel a Planck-scale vacuum energy against a bare constant to ~120 decimal places — has a real, checkable win: a one-line elementary theorem (L1, verified symbolically) shows the trace-free field equation annihilates any Lorentz-invariant vacuum energy pointwise, for any magnitude, so the ~$10^{121}$ never enters the equation that bends spacetime and there is nothing to tune. But the gate as a whole carries a sharp scope: the dissolution is conditional on one natural-but-unforced posit, the value $\Lambda=(2.3\,\text{meV})^4$ stays a measured anchor, and a second proven theorem (L2) shows the premise alone does not protect that value at the quantum level.

This page is the gate-specific instantiation of the anchoring method: it takes the master anchor and the four bridges and applies them, object by object, to one gate. Every exact thing this gate touches gets its own row — its status, what it is allowed to claim, and what it is forbidden to claim. It follows the same eleven-part shape and the same universal table as the canonical SG-4 ledger.

This gate is not shaped like an anomaly-ledger gate. There is no exact rational obstruction that vanishes on the frozen spectrum; the genuine win is a proven tensor identity that dissolves a pseudo-problem, plus an honest split of "radiative stability" into one positive sliver and two corrections. The page adapts honestly to that nature: the closed leg is a dissolution (dissolved $\neq$ solved), not a derivation.

1. Gate status header

• Gate-level Gap-05-catastrophe roll-up: DISSOLVED-GIVEN-root · RESOLVED +0 (board-canonical, ratified 2026-07-08; closure-of-record: the live gate dossier) — CATASTROPHE DISSOLVED (conditional; tree-level theorem PROVEN); the value & radiative-stability faces close in their companion gates (MEASURED-ANCHOR · RESOLVED +0; CERTIFIED-IRREDUCIBLE · RESOLVED +0), each with its residuals shown.
• Taxonomy reconciliation (2026-07-05): the gate-level grading is DISSOLVED-GIVEN-root · RESOLVED +0 (ratified 2026-07-08), read as TERMINAL + RESIDUALS-SHOWN (catastrophe-half = proven tree-level dissolution; value = legitimate measured anchor). The residual family listed in this ledger (value & radiative stability) remains carried unchanged; the facts are unchanged — the earlier OPEN roll-up (under the retired rule) reflects the superseded least-closed-residual rule, not different facts.
• The two faces, kept rigorously apart:
  • The catastrophe-half ("why isn't $\Lambda$ of order $M_{\rm Pl}^4$?") — the ~122-order discrepancy between the naive QFT estimate and the observed value. This is what the gate dissolves.
  • The value + radiative-stability half ("why this specific tiny number, and why does it stay small under ~122 orders of correction?"). Weinberg-open — the subject of the companion gates Gap-05-value and Gap-05-stability, each closed on the ratified board at its own honest terminal (MEASURED-ANCHOR · RESOLVED +0; CERTIFIED-IRREDUCIBLE · RESOLVED +0) with the Weinberg-open mechanism question carried as the shown residual.
• The closed local leg (a proven dissolution, not a derivation of $\Lambda$). For a Lorentz-invariant vacuum stress $T^{\rm vac}_{\mu\nu}=-V g_{\mu\nu}$, the trace-free source vanishes identically: $$ S_{\mu\nu}\;\equiv\;T^{\rm vac}_{\mu\nu}-\tfrac14 g_{\mu\nu}T^{\rm vac}\;=\;-V g_{\mu\nu}+V g_{\mu\nu}\;=\;0 . $$ This is L1 — DERIVED (PROVEN, verified symbolically), magnitude-blind, pointwise, robust under loops and across phase transitions. It is the gate's real win. It does not close the value-leg; it removes the catastrophe.

Status, split so it cannot be misread: - L1 — tree-level trace-drop: DERIVED (PROVEN) — an elementary, pencil-checkable tensor identity; the catastrophe-half is genuinely dissolved at the level of the local field equations. - The separating premise (trace-decoupling): AXIOM-OPEN / declared — a natural-but-unforced posit; not atomic, not forced. - L2 — premise alone is insufficient for the value: DERIVED (PROVEN as a negative) — an additive matter-loop shift maps identity onto the boundary datum; the value is radiatively shifted. - The value $\Lambda=(2.3\,\text{meV})^4$: MEASURED-ANCHOR — Tier-1, Weinberg-open, theory-laden; the gate's own prediction target and therefore never its own terminal.

selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique.

And, carried for this gate: dissolved ≠ solved · given-$\Lambda$ ≠ derivation-of-$\Lambda$.

2. Frozen inputs (what the gate stands on, not what it produces)

• Frozen branch hashes dcc66f1b2685 / a5b1e6f9d951. The branch is READ-ONLY and unmutated. These hashes are audit anchors — they certify which object was tested and that it cannot be quietly retuned. They do not validate the physics. The frozen 13D geometry produces no $\Lambda$, so no structure-side quantity is ever compared to $(2.3\,\text{meV})^4$ — the no-reverse-engineering from the measured value guarantee.
• The measured value $\Lambda=(2.3\,\text{meV})^4\approx 5\times10^{-10}\,\text{J/m}^3\approx 1\times10^{-122}\,M_{\rm Pl}^4$ is MEASURED-ANCHOR / charged — it enters as the observed total, extracted within $\Lambda$CDM. The gate does not derive it. Every "dissolves" below is a statement about the catastrophe, not a derivation of the value.
• Weinberg's 1989 no-go (Rev. Mod. Phys. 61, 1): no local, Poincaré-invariant field self-adjusts to cancel $\Lambda$ without fine-tuning, provided gravity couples to the full stress tensor (trace included). GIVEN / state-of-the-art bound — the gate evades it by declining its premise, not by violating it.

3. The object anchors (given / upstream)

The objects the gate acts on, tracked apart and never conflated:

The propagating degree of freedom is the same massless spin-2 graviton as GR; same null cones, same causal structure (GW170817: $c_{\rm GW}=c$ to $1$ part in $10^{15}$, automatically respected). Status: GIVEN / upstream-inherited — not gate-derived.

4. Root and master-anchor traceability

Deep roots that are load-bearing for this gate:

Shape and causal order are not primary load-bearing anchors here; the granularity / cost-floor lever is explicitly recorded wrong-shape (UV structure supplies contributions $\sim M_*^4$, the disease, not an IR cure) — an honest negative, not a hidden key.

Master anchors in play: the measured anchor (the $\geq 1$ floor — $\Lambda$ as boundary curvature) · no unpaid posit · the frozen branch (produces no $\Lambda$) · given-$\Lambda$ · the declared trace-decoupling premise · open-residual discipline · the no-reverse-engineering from the measured value firewall (the chamber route is a banked computed FAIL).

5. The Gap-05-catastrophe anchor ledger (the universal table)

6. The arithmetic / construction — the dissolution, in full

6.1 The hidden premise, and why gravity cannot test it

The catastrophe turns on three words: if it gravitates. To convert a QFT vacuum energy into a gravitational disaster you must feed $\rho_{\rm vac}$ into Einstein's equations as a source. Write the sources of the effective constant: $$ \Lambda_{\rm eff}=\Lambda_{\rm bare}+8\pi G\,\rho_{\rm vac}. $$ $\Lambda_{\rm bare}$ is a free geometric integration constant; $\rho_{\rm vac}$ is the zero-point hum. GR sees only their sum — both multiply exactly the same tensor $g_{\mu\nu}$ in exactly the same place. Two numbers that appear only ever added together, in identical positions, are one observable wearing a hand-imposed decomposition. The 1998 acceleration pinned $\Lambda_{\rm eff}\approx(2.3\,\text{meV})^4$; it said nothing — could say nothing — about the split. A universe with $\Lambda_{\rm bare}=(2.3\,\text{meV})^4$ and a non-gravitating $\rho_{\rm vac}$ is observationally identical to one with a gravitating $\rho_{\rm vac}$ delicately cancelled.

The precedent: everywhere outside gravity, only energy differences are physical. In QM this is exact — shift $H\to H+cI$ and the state picks up a global phase $|\psi(t)\rangle\to e^{-ict}|\psi(t)\rangle$; the Born squaring is phase-blind. The same phase-blindness that defines the Born rule makes absolute energy unobservable. Standard gravity is the lone law that breaks this blindness — and that single exception is the entire catastrophe.

6.2 The mechanism: unimodular gravity and the pointwise cancellation (L1)

The mechanism is not new physics — it is unimodular gravity (Einstein, 1919; flagged by Weinberg 1989 as a distinct CC-escape). Fix the determinant $\sqrt{-g}=$ fixed background volume form, so metric variations are traceless ($g_{\mu\nu}\delta g^{\mu\nu}=0$). This costs gravity one degree of freedom — the trace mode that rescales local volume, precisely the channel through which a constant vacuum energy talks to geometry. The ten Einstein equations are replaced by their trace-free part (nine independent equations): $$ R_{\mu\nu}-\tfrac14 g_{\mu\nu}R=8\pi G\big(T_{\mu\nu}-\tfrac14 g_{\mu\nu}T\big). $$

The load-bearing algebra (L1). A Lorentz-invariant vacuum energy can only enter as a term $\propto g_{\mu\nu}$ — forced, since $g_{\mu\nu}$ is the only Lorentz-invariant rank-two tensor at a point: $T^{\rm vac}_{\mu\nu}=-\rho\,g_{\mu\nu}$. Its 4D trace is $T^{\rm vac}=g^{\mu\nu}(-\rho g_{\mu\nu})=-4\rho$. Feed it into the trace-free source: $$ (-\rho g_{\mu\nu})-\tfrac14 g_{\mu\nu}(-4\rho)=-\rho g_{\mu\nu}+\rho g_{\mu\nu}=\mathbf{0,\ identically.} $$

(L1) PROVEN — tree-level trace-drop. For a vacuum stress $T^{\rm vac}_{\mu\nu}=-V g_{\mu\nu}$, the trace-free combination $T^{\rm vac}_{\mu\nu}-\tfrac14 g_{\mu\nu}T^{\rm vac}=0$ identically, for vacuum energy of any magnitude. The catastrophe-half is genuinely dissolved at the level of the local field equations — a real, elementary theorem, verified symbolically.

Three properties make L1 robust, each load-bearing for §6.4: 1. Magnitude-blind. $\rho$ never enters; it factors out and subtracts against itself. Whether $\rho=(2.3\,\text{meV})^4$ or the full Planck $3\times10^{11}\,\text{J/m}^3$, the result is the same zero. The size — the whole problem in standard GR — is irrelevant. 2. Pointwise. An algebraic identity at each event independently. No integral, no averaging over history, no boundary to reach. 3. Insensitive to time-dependence. If $\rho\to\rho(t)$ the source is still $\rho(t)g_{\mu\nu}$, still $\propto g_{\mu\nu}$, so its trace-free part is still identically zero, instant by instant.

Where $\Lambda$ comes back. The trace-free equations discard the one equation that fixed the absolute scale. Taking the covariant divergence and using conservation + the Bianchi identity integrates them once, recovering $G_{\mu\nu}+\Lambda_{\rm int}g_{\mu\nu}=8\pi G\,T_{\mu\nu}$, where $\Lambda_{\rm int}$ is a single global integration constant fixed by boundary data — not the vacuum energy. There is no 120-digit sum to cancel because the large term was never added.

Diagnostic — the result is specific, not vacuous. L1 is not the trivial statement "any tensor has zero trace-free part." The cancellation is specific to the pure-trace structure: a non-pure-trace source survives. Radiation ($w=1/3$) is not $\propto g_{\mu\nu}$, so its trace-free part is non-zero and it gravitates normally — which is exactly why the latent heat released at a phase transition (§6.4, Test 2) correctly gravitates and standard cosmology (BBN) is untouched. That the projector annihilates the vacuum's pure-trace stress while passing radiation's non-trace stress is what makes L1 a real structural fact rather than an artifact.

6.3 Radiative stability: the honest three-layer split (L1 / L2 / L3)

A first instinct is to declare the value protected too. This is an over-reach, and the corpus caught its own slogan. The verified theorem is a three-layer split. L1 (above) is the positive sliver. L2 and L3 are the honest corrections.

(L2) PROVEN — the premise ALONE is INSUFFICIENT at the quantum level. Under the premise the field equations recover standard GR with $\Lambda$ entering as a globally-fixed integration constant $\Lambda_0$. But an additive matter-loop vacuum shift $\mathcal L_m\to\mathcal L_m+\delta V$ passes straight through to that boundary datum: $\Lambda_0\to\Lambda_0+\delta V$ (the map is the identity). The slogan "an integration constant has no beta function, so there is nothing to renormalize" is true but irrelevant — there is no running coupling, yet the boundary value is shifted additively (Padilla–Saltas arXiv:1409.3573). The requested all-orders cancellation is FALSE for the separating premise alone.

(L3) CONDITIONAL — all-orders sequestering holds only for a strictly heavier construction, and only given an unproven assumption. The Kaloper–Padilla mechanism (arXiv:1606.04958) — gravity augmented with rigid global scalars, a Gauss–Bonnet term, and global flux / 4-volume constraints — does deliver an all-orders cancellation including virtual gravitons, but only conditional on a smoothness/non-degeneracy assumption $S$, established "in the action" rather than order-by-order, with background-curvature corrections asserted (not proven) harmless. It is strictly stronger than the separating premise, so it relocates the premise to a heavier conditional posit — it does not derive it.

The crucial scope distinction, stated once so it is never blurred: "survives all loop orders" is TRUE for the catastrophe-half (L1's tensor identity is loop-stable) and FALSE if read as "the value is radiatively protected by the premise alone" (L2 refutes that). This exact phrasing risk is logged as Hole 7.

6.4 The two physical stress tests, and the mechanism comparison

Test 1 — radiative (loop) stability of the catastrophe-half. The cancellation is algebraic in the tensor structure, not arithmetic in the magnitude. A loop correction changes the magnitude of the vacuum energy; it does not change its tensor character. Whatever the electron, the QCD condensate, or the electroweak sector contributes is still Lorentz-invariant, hence $\propto g_{\mu\nu}$, hence pure trace, hence annihilated pointwise — at one loop, two loops, every loop, at every threshold from $m_e$ up. There is no number in it to destabilize. Moreover UG's quantum effective action is itself unimodular (Padilla–Saltas arXiv:1712.09903; Smolin arXiv:0904.4841). Caveat (logged): the all-orders claim is inherited from the static-case literature; time-dependence was verified to introduce no new failure channel, but the static all-orders result was not independently re-derived (Hole 3). Verdict: DISSOLVES-CATASTROPHE, SURVIVES-LOOPS — no value smuggled; matter/light intact; Weinberg evaded; value unexplained.

Test 2 — the phase transitions (the make-or-break). Across the QCD ($\sim150\,\text{MeV}$) and electroweak ($\sim100\,\text{GeV}$) transitions the condensate changes in time; a leak of order $\Lambda_{\rm QCD}^4$ ($\sim10^{44}\times\Lambda_{\rm obs}$) or $v^4$ ($\sim10^{55}\times\Lambda_{\rm obs}$) would kill the reframe: - A time-varying $\rho_{\rm vac}(t)g_{\mu\nu}$ is still $\propto g_{\mu\nu}$ at each instant, so its traceless part is identically zero at every $t$ (verified over a $t$-sweep; max residual $0$). - The condensate is not separately conserved while changing ($\nabla^\mu T^{\rm vac}_{\mu\nu}=-\partial_\nu\rho_{\rm vac}\neq0$); by total conservation the released latent heat flows into radiation/particles, which gravitates correctly ($w=1/3$ is non-pure-trace) — the wanted kind of leak; BBN safe. - Wrongly-gravitating residual $\approx0$; largest surviving non-trace leftover today $\sim10^{-13}\,\text{J/m}^3\approx10^{-4}\,\Lambda_{\rm obs}$ — too small to be $\Lambda$. - The integration constant $\Lambda_{\rm int}$ is uncontaminated by the epoch jumps (the jump lives in the dynamical $(R,T_{\rm tot})$ pair, not the constant).

The "necessary-conditions ledger" makes explicit that four of five conditions are automatic (Lorentz+translation invariance; Bianchi; UG structure; the algebraic identity), and everything collapses onto condition #5: gravity decouples the trace pointwise/locally — the load-bearing posit. That single posit is the entire conditionality of the result.

Mechanism comparison — the clean survival is unimodular-specific:

Across all three: latent heat gravitates correctly, BBN safe, no value-smuggling — none predicts the dark-energy density. The special ingredient is the pointwise/local trace-decoupling; UG is its minimal carrier.

Weinberg evaded, legitimately. UG contains no self-adjusting field at all; it changes the coupling (gravity sees $T_{\mu\nu}-\tfrac14 g_{\mu\nu}T$, not $T_{\mu\nu}$), so the central hypothesis of the no-go — gravity sees the full trace — is simply false here. You cannot violate a theorem whose premise you decline. And this is not a loophole — Weinberg himself flagged trace-decoupling as a distinct, legitimate route.

7. Declared-structure splits — why "radiative stability" is three objects, not one

The single phrase "radiatively stable" hides three distinct claims with three statuses, and the proposal to collapse them was corrected:

1. Catastrophe-half loop-stability — the absolute-level non-gravitation survives loops because L1 is about tensor structure, not magnitude. Status: DERIVED-GIVEN-premise (true).
2. Value radiative-protection by the premise alone — that $\Lambda_0$ is shielded from matter loops. Status: REFUTED by L2 — $\delta V\to\Lambda_0$ is the identity map.
3. All-orders value-protection including virtual gravitons — exists only in the strictly heavier L3 construction, conditional on assumption $S$. Status: CERTIFICATE-CONDITIONAL.

A second split, inside the premise: the trace-decoupling posit (declared, AXIOM-OPEN) is distinct from its uniqueness/minimality (R-uniqueness, OPEN, Hole 1) and from any consistency-forcing (the quantization route, AUDIT / NO-FORCING, Hole 4). Naming the posit does not reduce the axiom count; only Hole 1 or Hole 4 could upgrade "natural choice" to "forced."

8. The no-reverse-engineering from the measured value firewall — guard against true-by-construction

A dissolution counts only if no structure-side quantity was ever tuned to the answer. The frozen 13D geometry produces no $\Lambda$; all four dissolution builds were hunted for $(2.3\,\text{meV})^4$ and it is never back-solved. Two adversarial reduce-attacks were run and failed (the honest outcome): (1) granularity — a finite supertrace $\sim M_{\rm cut}^4$ at $M_{\rm cut}=1/R_0$ is off by $\sim113$ orders and predicts no value; (2) implicit-assumption audit — no known assumption-drop predicts it.

Most tellingly, the corpus's own sign-graded chamber-cancellation route is a computed FAIL: the $\Lambda$ operator is the unit/identity operator — grading-even, label-blind — so no chamber-label grading can act on it (quantitative witness: $0.58$ residual at $k=0$). Reported as a loss — and that loss is consistent with the dissolution: cancellation was never needed, because once the trace decouples there is no $10^{121}$ to cancel. A theory that needed the chamber route would be in trouble; this one predicts it should fail, and it does. (The two seductive coincidences $\kappa^3/\pi$ and $5+3=8$ are RETIRED cautionary examples; they belong to BG-10, never banked here.)

9. Open residuals — the families, each its own row

Grouped, never collapsed. None is closed by the L1 dissolution.

Forcing the premise (the highest-leverage family): - Hole 1 — R-uniqueness (highest value). Is freezing the metric volume/trace mode the unique minimal structural change that decouples the trace while leaving local GR intact? OPEN — the only path that could upgrade the premise from "natural conjecture" to "forced (but still unmeasured)." - Hole 4 — quantization obstruction on the gauged trace mode. The named "most credible undeveloped route" to upgrade "need not exist" to "cannot exist." AUDIT / NO-FORCING (banked): the first pass returned a clean negative (the conformal-factor problem is curable within full GR).

Radiative stability of the value: - Hole 2 — sequestering condensate residual (R5). The finite EW/QCD shifts must be shown genuinely sequestered, not merely dropped. OPEN. L1 kills the pure-trace part, not the finite history-dependent remainder (the exact L1↔value scope error L2 guards against). - Hole 3 — all-orders graviton-loop / sequestering (R5′). An order-by-order replacement for L3's "in-the-action" argument, plus a proof of assumption $S$. OPEN / certificate-conditional. Does not touch the value (L2: $\delta V\to\Lambda_0$ is the identity). - Hole 5 — burden-predicate soundness/completeness (R6). The soundness/completeness check of the R1–R4 harness against the ~122-order burden is owed. AUDIT / BLOCKED.

Cascade + editorial: - Hole 6 — non-perturbative-QCD condensate tie (R7). An R4/R5 evaluation may depend on non-perturbative QCD, cascading to the Gap-02 / UQF-11 family. OPEN (upstream) — not closeable inside Gap-05. - Hole 7 — public-copy scoping risk (editorial). The phrase "survives all loop orders" is correct as a catastrophe-half claim but read loosely could imply value-protection (which L2 refutes). OPEN / editorial — a wording fix, not a derivation.

10. Anti-claims (what this page refuses to say)

• The gate does not derive $\Lambda$. $\Lambda=(2.3\,\text{meV})^4\approx10^{-122}M_{\rm Pl}^4$ remains a MEASURED-ANCHOR, theory-laden, Weinberg-open. Because $\Lambda$ is also the gate's own prediction target, by the anchor-vs-target rule it can never be the terminal that closes its own value-leg. ANCHORED ≠ DERIVED; given-$\Lambda$ ≠ derivation-of-$\Lambda$.
• Dissolved ≠ solved. The "new" cosmological-constant problem — why this specific small value, and why now — is untouched and stays OPEN.
• The premise alone does not protect the value. L2 is PROVEN: $\Lambda_0\to\Lambda_0+\delta V$ is the identity map. "The value survives all loop orders / is radiatively protected by the premise" is the over-claim a frozen doc denies.
• The dissolution is not forced. Trace-decoupling is AXIOM-OPEN / declared. Standard GR with a tuned bare $\Lambda$ is perfectly consistent and observationally identical — its only flaw is being infinitely unnatural, and "unnatural" is not a law of physics. The result is terminal at elegance.
• L1 does not kill the finite condensate shift — only the pure-trace part; the finite history-dependent remainder is the open R5 work (conflating them is exactly the L1↔value scope error).
• L3 does not derive the premise — it is strictly stronger and relocates it to a heavier conditional posit given assumption $S$.
• The chamber-cancellation route does not derive $\Lambda$ — it is a banked computed FAIL ($\Lambda$ is the identity operator); the failure corroborates the dissolution, it does not undermine it.
• The frozen-branch hashes are audit anchors; they do not validate the physics, and the frozen geometry produces no $\Lambda$.

11. Specialist closure plan

Each open residual is a concrete, finite, target-blind work-package; each carries the no-reverse-engineering from the measured value falsification test (a regulator or measure reverse-engineered to make $\Lambda$ appear is true-by-construction and relocates rather than closes).

1. Hole 1 (R-uniqueness) — classify local, generally-covariant modifications preserving local Einstein dynamics and show trace-decoupling is the unique minimal survivor under a pre-declared, architecture-neutral minimality metric. Machinery: Lovelock-type uniqueness theorems; Henneaux–Teitelboim / Ellis UG formulations; the three carriers (UG, global sequestering, local sequestering) as a partial enumeration. Trap: do not define minimality so volume-mode-freezing wins by construction; do not chase the absolute unicorn. Refuting outcome (equally valid): a second inequivalent minimal modification that also decouples the trace — shows the premise is "one of many." Closing this is the single biggest available move, and it is the same R-uniqueness object shared by Gap-05-value and Gap-05-stability.
2. Hole 2 (R5 condensate residual) — explicit finite computation that the EW/QCD shifts are sequestered by the volume-constraint mechanism with latent heat gravitating correctly. Success: wrongly-gravitating residual bounded $\leq\Lambda_{\rm obs}$ across the real thermal history. Machinery: Kaloper–Padilla global sequestering (arXiv:1309.6562, 1406.0711); the App. B/C phase-transition numbers. Trap: do not appeal to L1 alone — it kills the pure-trace part, not the finite remainder.
3. Hole 3 (all-orders / R5′) — a BPHZ-type order-by-order proof replacing the "in-the-action" argument, plus a proof of assumption $S$, plus a proof that background-curvature corrections are harmless. Machinery: BPHZ renormalization; the Kaloper–Padilla augmented action (arXiv:1606.04958). Trap: do not let a regulator do the cancellation; do not present L3 as deriving the premise. Refuting outcome: a finite uncancelled graviton-loop contribution — narrows the all-orders claim, a valid close.
4. Hole 4 (quantization obstruction) — find a genuinely new obstruction (a non-perturbative anomaly or measure pathology specific to gauging the trace) that survives the three known cures (Gibbons–Hawking–Perry contour rotation; Mazur–Mottola covariant measure; Marolf–Santos real-time construction) and the ADM-absence observation. Success: a demonstrated quantum pathology with no in-theory cure → trace-decoupling promoted from posit to consistency requirement (the upgrade to "cannot exist"). Trap: do not re-run the conformal-factor version (closed); do not slide to the universal-negative unicorn. Refuting outcome (current best evidence): confirmation that every candidate obstruction is curable → the route stays closed and the result stays "terminal at elegance."
5. Hole 5 (R6 burden predicates) — run the soundness/completeness check on R1–R4 against the ~122-order burden ($(\Lambda/M_{\rm Pl})^4\approx1.26\times10^{-123}\to{\sim}122.90$ orders with the full Planck mass; $\approx7.96\times10^{-121}\to{\sim}120.07$ orders reduced) and report it. Trap: the harness checks bookkeeping, not the world; do not fabricate a verdict.
6. Hole 6 (R7 non-perturbative tie) — resolve the exported condensate-shift dependence inside the UQF-11 family; not closeable inside Gap-05. Bounded by that gate's progress; cross-links to Gap-02 mass-gap.
7. Hole 7 (editorial scope) — tighten every public surface carrying "survives all loop orders" to the absolute-level non-gravitation (catastrophe-half) and explicitly disclaim value-protection by the premise alone. An editorial fix, not a derivation.

Closing Hole 1 or Hole 4 upgrades the catastrophe-half from "DISSOLVED (conditional)" toward "DISSOLVED (forced premise, still unmeasured)" — and even then, the value stays a measured anchor.

12. Completion tests for this page

Required presence (all met): gate roll-up DISSOLVED-GIVEN-root · RESOLVED +0 — CATASTROPHE DISSOLVED (conditional); value MEASURED-ANCHOR in its companion gate · the closed local leg $T^{\rm vac}_{\mu\nu}-\tfrac14 g_{\mu\nu}T^{\rm vac}=0$ · L1 DERIVED (PROVEN) with the magnitude-blind/pointwise/time-insensitive properties · the radiation diagnostic (non-pure-trace stress survives) · $\Lambda$ not derived (MEASURED-ANCHOR, Weinberg-open) · frozen hashes AUDIT ONLY (produce no $\Lambda$) · $\Lambda_{\rm eff}=\Lambda_{\rm bare}+8\pi G\rho_{\rm vac}$ (sum-only) · the trace-free field equation · L2 PROVEN-negative · L3 CERTIFICATE-CONDITIONAL on assumption $S$ · the two stress tests (loops; phase transitions) · the mechanism comparison · Weinberg evasion · the chamber-route banked FAIL · the no-reverse-engineering from the measured value firewall · every Hole 1–7 as its own residual · the gate's anti-claims · dissolved-unicorn ceilings (in §11 traps / anti-claims).

Required absence (all held): no claim that the cosmological-constant problem is solved · $\Lambda$ derived/closed · the value radiatively protected by the premise alone · trace-decoupling forced · L1 kills the finite condensate shift · L3 derives the premise · the chamber route derives $\Lambda$ · any open residual asserted proven/computed/closed · hashes validate physics · dissolved = solved · any reader-visible build-process vocabulary.

Completion report. Tests passed: all required-presence and required-absence items above. Tests failed: none. Open items: Holes 1–7 (the gate's named residuals) + the two dissolved unicorns (shared ceilings, not work). Assumptions made: none beyond the frozen branch and the single declared trace-decoupling premise; nothing here upgrades the gate's grade.

Binding closing statement. Gap-05-catastrophe is CATASTROPHE DISSOLVED (conditional; tree-level theorem PROVEN) — the value and radiative-stability faces close in their companion gates at their own honest terminals (MEASURED-ANCHOR · RESOLVED +0; CERTIFIED-IRREDUCIBLE · RESOLVED +0), each with its Weinberg-open mechanism question carried as the shown residual. The genuine, non-promoting win is L1: the trace-free part of any pure-trace vacuum stress is identically zero, for any magnitude, pointwise, robust under loops and across phase transitions — so the $\sim10^{121}$ never bends a single ray of light and there is no 120-digit tuning to perform. The premise (trace-decoupling) is a natural-but-unforced declared posit; the value $\Lambda=(2.3\,\text{meV})^4$ stays a measured Tier-1 anchor (Weinberg-open); and L2 proves the premise alone does not protect that value. Ceiling: a serious, defensible candidate — terminal at elegance, NOT validated. Frozen branch dcc66f1b2685 / a5b1e6f9d951 READ-ONLY and unmutated; selection ≠ derivation · given-E ≠ derivation-of-E · frozen/reproducible ≠ proven-unique · dissolved ≠ solved · given-$\Lambda$ ≠ derivation-of-$\Lambda$.

This gate anchor ledger follows the canonical eleven-part shape and universal table of the SG-4 ledger.

See also: the anchoring method · A0 — the master anchor · Layer 2 — no unpaid exact labels (why anomaly cancellation — and a tuned bare $\Lambda$ — is a filter, not a selector) · the Born rule ledger (the same phase-blindness that makes absolute energy unobservable) · SG-4 — Hypercharge & anomaly (the canonical gate ledger) · the full Gap-05-catastrophe dossier.