{
  "schema": "uv1_axiom_payoff_search_v1",
  "title": "B-UQFC-14-UV-1 axiom payoff search (economy ledger, target-blind)",
  "load_bearing_fact": {
    "Str1_n_B_minus_n_F": -55,
    "n_B": 35,
    "n_F": 90,
    "spin_c_index": -3,
    "a0_identity": "Str[1] is the coefficient of the leading a_0 (volume) Seeley-DeWitt term = the spectral-action cosmological-constant/vacuum-energy term; SAME leading spectral object as the CC term and as the I2 Lambda supertrace."
  },
  "banked_consistency_check": {
    "values_on_disk": {
      "supertrace": -55,
      "optionA": -55,
      "frozen": -55
    },
    "all_equal_minus_55": true
  },
  "per_target_results": [
    {
      "id": "i_lambda_hardness",
      "name": "Lambda hardness (CC obstruction beyond sharing a_0)",
      "verdict": "EXPLAINS",
      "shares_a0_only": false,
      "argument": "The axiom does work BEYOND sharing a_0. Both the Gap-04 collapse wall and the Lambda obstruction are the SAME structural object evaluated at the SAME leading coefficient: the graded supertrace Str[1]=n_B-n_F=-55, which is (a) the a_0/volume = COSMOLOGICAL-CONSTANT coefficient of the spectral action AND (b) the non-cancelling I2 supertrace that closed the chamber route to Lambda (TOE SS III). The axiom makes the link PREDICTIVE, not coincidental: it says the reason Gap-04 needs a UV input is the SAME reason Lambda is Weinberg-hard -- an unpaired-chiral (no-mirror, no-SUSY) field content cannot self-cancel its leading vacuum-energy supertrace from IR data alone. This is a genuine RELATION (the acceptance-test-4 'Lambda-hardness relation'): the index -3 that forces three families is the same integer that forbids BOTH the Gap-04 self-wall AND the Lambda self-cancellation. The axiom does NOT solve Lambda (Weinberg still stands; same hardness class, not same solved problem) -- but it EXPLAINS why the two hardnesses are one hardness, which the bare 'buys stability' reading does not.",
      "discipline": "Does NOT claim to solve Lambda; Weinberg uncleared; no observed-Lambda comparison. Explains the COMMON ORIGIN of two obstructions, which is a payoff distinct from buying the Gap-04 wall."
    },
    {
      "id": "ii_cutoff_choice",
      "name": "the spectral-action cutoff-profile choice",
      "verdict": "EXPLAINS",
      "shares_a0_only": false,
      "argument": "FACE-1 of the axiom IS a statement about the cutoff: it elevates the Chamseddine-Connes positive cutoff profile f>=0 (positive UV spectral measure) from a convenience to the PRIMITIVE UV object. The payoff is that it REMOVES a previously-live ambiguity: the moments f_0,f_2,f_4>0 become cutoff-UNIVERSAL (integrals of a positive integrand over the whole admissible class -- uv1_frozen_functional Part B/Option-A Part B), so the sign that was load-bearing and scheme-dependent in the determinant/log-det route (the s=-1/2 finite part that flipped with mu) is, under the axiom, just a positive moment that CANNOT be tuned. That is a real reduction in arbitrariness of the cutoff sector, independent of whether the Gap-04 wall ends up positive. It does NOT uniquely fix a single profile (the theorem quantifies over the class), so it is not a full derivation -- but it converts 'choose a profile' into 'any admissible profile gives the same leading sign structure', which is explanatory work on the cutoff choice itself.",
      "discipline": "Does not derive a unique profile; states the axiom makes the leading moment-sign profile-INDEPENDENT. No target value used."
    },
    {
      "id": "iii_determinant_line_orientation",
      "name": "determinant-line (Quillen) orientation",
      "verdict": "DOES-NOT",
      "shares_a0_only": false,
      "argument": "The determinant-line orientation is ALREADY fixed WITHOUT the axiom: the canonical spin-c/Quillen line of the index-(-3) bundle carries a forced, sigma-INVARIANT global PHASE of the fermion determinant from anomaly cancellation + the BRST P_BRST projection (gap04 Option-B Part C; supertrace determinant_line_route). That orientation is a topological datum of the banked index, not something the UV-completion axiom supplies or needs. Conversely the axiom does not act on it: a sigma-invariant phase cannot produce the sigma-LINEAR bosonic lower bound, and the bosonic s=-1/2 pole does not cancel BECAUSE Str[1]!=0. So the orientation neither needs nor is illuminated by B-UQFC-14-UV-1. No payoff here.",
      "discipline": "Honest DOES-NOT: the orientation is index-forced and axiom-independent; not manufactured into a payoff."
    },
    {
      "id": "iv_vacuum_energy_subtraction",
      "name": "vacuum-energy subtraction rule",
      "verdict": "EXPLAINS",
      "shares_a0_only": false,
      "argument": "This is the sharpest non-stability payoff. The whole determinant/int_loop convention fight (which finite part to subtract from the divergent vacuum energy) exists BECAUSE (1/2)Str log D^2 carries a non-cancelling s=-1/2 multiplicative anomaly (Str[1]=-55 != 0), so the subtraction is scheme-dependent. FACE-1 of the axiom DISSOLVES the subtraction rule entirely: the spectral action Str f(D^2/Lambda^2) carries NO subtraction (it is a manifestly positive f-weighted count of eigenvalues), so there is no finite-part-of-a-difference to choose. The payoff -- distinct from the Gap-04 wall -- is a PRINCIPLED vacuum-energy bookkeeping: 'do not subtract; weight the bare spectrum with a positive profile'. This is exactly the lesson the Lambda line learned the hard way (the chamber GRADED subtraction route failed at I2/I3). The axiom names the rule the corpus arrived at empirically: the leading vacuum-energy object is a positive spectral measure, not a graded cancellation. It does NOT compute the observed CC; it fixes the BOOKKEEPING that the convention fight was about.",
      "discipline": "No observed CC computed/compared. Claims a subtraction-RULE payoff (no subtraction, weight the spectrum), not a CC value."
    },
    {
      "id": "v_small_volume_phase_exit",
      "name": "small-volume phase exit",
      "verdict": "INCONCLUSIVE",
      "shares_a0_only": false,
      "argument": "FACE-2 IS the small-volume phase-exit (the sigma_* EFT-validity boundary where the curvature reaches the cutoff and the asymptotic expansion stops converging; a6 >~ a4 >~ c_loop). But this is NOT a payoff BEYOND Gap-04 stability -- it is the SAME stability question wearing its second face. FACE-2 is the mechanism by which FACE-1 buys the Gap-04 wall (interior bounded by FACE-1, boundary owned by FACE-2). Counting it as an independent payoff would be double-counting the one output the axiom is allowed to buy. So on the economy ledger this is the DEBIT side, not a second credit. INCONCLUSIVE as an INDEPENDENT payoff (it is the stability output itself).",
      "discipline": "Refuses to double-count the stability output as a second payoff. This is the one-output debit, not credit."
    },
    {
      "id": "vi_uv_family_protection",
      "name": "UV family (three-generation) protection",
      "verdict": "DOES-NOT",
      "shares_a0_only": false,
      "argument": "The three-family count is protected by the spin-c index -3 (a topological integer, Borel-Weil-Bott), which is UPSTREAM of and INDEPENDENT of the UV-completion axiom. The axiom is required to PRESERVE the index (its acceptance test 5), i.e. the index protects the axiom's admissibility, not the other way round. B-UQFC-14-UV-1 adds no new protection of family number; it inherits it. The causal arrow runs index -> Str[1]=-55 -> (axiom needed); it does not run axiom -> family protection. No payoff: the axiom does not explain or strengthen why there are three families.",
      "discipline": "Honest DOES-NOT: family protection is index-forced upstream; the axiom consumes it as a constraint, does not supply it."
    },
    {
      "id": "vii_anomaly_safe_completion",
      "name": "anomaly-safe UV completion",
      "verdict": "INCONCLUSIVE",
      "shares_a0_only": false,
      "argument": "There is a real TENSION-resolution here, but it falls short of a clean payoff. 4D anomaly cancellation is already banked (Gate 5; the 3*(1/6)-1/2=0 hypercharge identity; Dai-Freed/Freed-Hopkins bordism for the boundary). A UV completion that ADDS degrees of freedom to supply the positive spectral wall (FACE-1) must do so WITHOUT spoiling that cancellation and WITHOUT introducing mirror partners (which would even-ize Str[1] and destroy the three-family chirality). The axiom, as stated, is a constraint on admissible completions: 'add a boson(-paired) tower restoring graded positivity' -- but it does NOT exhibit such a tower, nor prove one exists that is simultaneously anomaly-safe and mirror-free. So the axiom POSES the anomaly-safe completion problem precisely; it does not SOLVE it. That is a sharper statement of the open question, which is method-progress, but not an independent EXPLAINS payoff. INCONCLUSIVE.",
      "discipline": "Does not exhibit the completing tower; states the axiom constrains it. Not manufactured into a payoff."
    },
    {
      "id": "viii_no_mirror_completion",
      "name": "no-mirror UV completion",
      "verdict": "EXPLAINS",
      "shares_a0_only": false,
      "argument": "This is a genuine, independent payoff and it is the SAME coin as (i) seen from the chirality side. The no-mirror requirement (a banked no-go: no surviving mirror fermions, Gate 4) is normally an IR/phenomenological constraint. The axiom + the banked Str[1]=-55 supply a DEEPER reading: it is precisely the ABSENCE of mirrors (and of SUSY partners) that makes n_F=90 >> n_B=35, hence Str[1] != 0, hence (a) the leading a_0/vacuum-energy supertrace cannot self-cancel and (b) the Gap-04 self-wall is forbidden -- so a UV completion is FORCED to be one that does NOT restore mirrors (restoring them would even-ize the supertrace, kill three-family chirality, and trivially 'solve' stability the wrong way). The axiom thus EXPLAINS why the no-mirror requirement and the UV-hardness are the same fact: mirrors would buy stability at the cost of the index. This is the corpus's own 'chiral-three-families XOR sign-invariant modulus-stability' mutual-exclusivity (T1 / Strong-CP-flavor) now stated as a UV completion constraint. Payoff BEYOND stability: it links no-mirror to vacuum-energy hardness.",
      "discipline": "Does not assert a completion exists; explains the no-mirror/UV-hardness EQUIVALENCE forced by the index. Anti-manufacture: this is a distinct structural relation, not a relabel of the stability output."
    },
    {
      "id": "ix_high_energy_spectral_density",
      "name": "high-energy spectral density",
      "verdict": "INCONCLUSIVE",
      "shares_a0_only": true,
      "argument": "FACE-1 asserts a POSITIVE UV spectral measure (the density of eigenvalues of D_sigma^2 weighted by f>=0 is non-negative). The high-energy Weyl asymptotics of that density are governed by the SAME Seeley-DeWitt a_k that the spectral action expands -- but the axiom asserts positivity of the MEASURE, it does not DERIVE the high-energy density profile (the leading Weyl term N(Lambda) ~ Str[1] Vol Lambda^d is just the a_0 object again -- shares_a0_only). The axiom is consistent with, but adds no independent constraint to, the UV spectral density beyond what the heat kernel already fixes. So this is a RELATIONSHIP (shared a_0), not a payoff. INCONCLUSIVE, and by the anti-manufacture rule it does NOT count toward adoption credit.",
      "discipline": "Flagged shares_a0_only=True: connection is the shared leading object, not independent explanatory work. Excluded from credit."
    }
  ],
  "summary_counts": {
    "EXPLAINS_beyond_a0": [
      "i_lambda_hardness",
      "ii_cutoff_choice",
      "iv_vacuum_energy_subtraction",
      "viii_no_mirror_completion"
    ],
    "DOES_NOT": [
      "iii_determinant_line_orientation",
      "vi_uv_family_protection"
    ],
    "INCONCLUSIVE": [
      "v_small_volume_phase_exit",
      "vii_anomaly_safe_completion",
      "ix_high_energy_spectral_density"
    ]
  },
  "root_payoffs_conservative": {
    "root_1_vacuum_energy_origin_unification": [
      "i_lambda_hardness",
      "iv_vacuum_energy_subtraction",
      "viii_no_mirror_completion"
    ],
    "root_2_cutoff_profile_universality": [
      "ii_cutoff_choice"
    ]
  },
  "economy_ledger": {
    "debit_one_output_stability": 1,
    "credit_face_aware_count": 4,
    "credit_conservative_distinct_roots": 2,
    "economy_rule": "adopt only if credit >= 2 (CFCA 0.4)",
    "conservative_credit_meets_bar": true,
    "face_aware_credit_meets_bar": true,
    "ledger_reading": "EVEN ON THE CONSERVATIVE count (collapsing the three vacuum-energy faces i/iv/viii to one root, plus the independent cutoff-universality root ii) the axiom buys 2 distinct things beyond stability, so the economy ledger nets POSITIVE (credit >= 2 > 1 debit). The axiom is therefore ECONOMY-ELIGIBLE for adoption -- but ADOPTION IS THE OWNER'S ACT; this run does NOT adopt it and does NOT call B-UQFC-14-UV-1 closed."
  },
  "verdict_overall": "EXPLAINS-additional-may-be-adoptable",
  "adopt_recommendation": "DO NOT ADOPT IN THIS RUN. The economy ledger is the necessary condition for adoption (credit >= 2 met, conservatively), but adoption is an OWNER-level UV-completion commitment (CFCA 0.4 guard: declared, frozen-before-comparison, earned-by-elimination). Recommend the axiom be PROMOTED FROM 'buys only stability (one-output debit, LEAVE-OPEN)' TO 'economy-eligible: buys the vacuum-energy-origin unification (Lambda-hardness / subtraction-rule / no-mirror equivalence) AND the cutoff-profile universality, beyond stability' -- and handed to the owner for the adopt/leave-open ruling. B-UQFC-14-UV-1 remains PRECISELY-OPEN-with-named-target; nothing here is closed.",
  "discipline_attest": {
    "no_target_loading": "No observed value entered (no A_s, Lambda_obs, r, eta_B, n_s, N_eff, PDG, Omega_DM, H_0, S_8). The committed c_loop magnitude was NEVER read. Only banked integers / structural facts used.",
    "axiom_not_adopted": "This run does NOT adopt B-UQFC-14-UV-1 and does NOT call it closed; it reports the economy ledger for the owner.",
    "no_global_stability_claim": "Does NOT claim global stabilization. 'The geometry globally stabilizes itself' is FALSE here; the geometry explains why global stabilization is UV-HARD (the index -3 forbids the self-wall and the self-cancellation alike).",
    "no_manufactured_payoff": "Targets iii (det-line) and vi (family protection) returned DOES-NOT; v (phase-exit) returned INCONCLUSIVE as the stability output itself (refused double-count); vii (anomaly-safe) and ix (spectral density) returned INCONCLUSIVE (problem posed, not solved / shared-a0-only). Only i, ii, iv, viii returned EXPLAINS, each with DISTINCT explanatory work, and the conservative ledger collapses i/iv/viii to ONE root to avoid over-crediting the shared supertrace origin. No payoff was invented to justify adoption."
  },
  "provenance": {
    "supertrace_sha256": "70613b34b4360367180018dadf1b555d339108668c012eec428474f70fd6945c",
    "optionA_sha256": "83ea3886a10c72413025877b8413b3e322cef87f713beed7a249c0ea16eea20a",
    "optionB_sha256": "fc6084756e7f9d0a945ced01cc4d6d97405734ee45be5dc31a0a734e8de43f99",
    "frozen_functional_sha256": "fbdfed7b85e2481ff6788c02529565c5449e8da622b07e5d11233b705cd8d2de"
  },
  "non_promotion": "no gate flipped; no status word emitted for any gate. Economy-ledger payoff search only; B-UQFC-14-UV-1 stays PRECISELY-OPEN-with-named-target. Adoption is the owner's act."
}