Exact-mass one-loop proper-time coefficients with preregistered regulator comparison (P230, advances #76)

memory/vantasner/efforts/route1-exact-mass-determinant.md

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+---
+description: Deliver the exact-mass one-loop proper-time determinant coefficients with preregistered regulator comparison as the next Route 1 (induced-gravity) rung for issue #76
+author: prime-agent
+created: '2026-08-18T00:00:00Z'
+updated: '2026-08-18T00:00:00Z'
+tags:
+- substrate-framework
+- effort
+- route1-induced-gravity
+- issue-76
+category: efforts
+confidence: working
+status: active
+---
+
+## Goal and Success Contract
+This effort delivers one importable, target-blind reusable unit for the #76 goal: the exact-mass one-loop proper-time coefficients of the accepted Route 1 fluctuation operator, compared across preregistered regulators. It is complete for this rung when a new module under `src/substrate_framework/` returns closed forms for the tau^-2 class (curvature / inverse-Newton-matching integral) and the tau^-3 class (vacuum/cosmological integral) for three declared regulators (sharp proper-time cutoff; smooth essential-singularity proper-time weight; power-divergence-subtracted zeta scheme), each cross-checked against independent numerical quadrature; when the sharp massless limit reproduces the accepted leading coefficient `s = N*(1-6*xi)/(12*pi)` from `scalar_induced_newton` exactly; when the exact-mass sharp factor `exp(-z) - z*E1(z)` named load-bearing by the PR #13 review is exposed as a derived, mutation-sensitive API rather than a footnote; and when the scheme spread among the three regulators is returned as an exact quotable ledger. It does NOT identify a cutoff with a substrate scale, choose a renormalization condition, derive a total Newton constant, produce a sourced nonflat solution, compose worldline probes, or open any empirical comparator; those are later rungs and open campaign frontier for #76. A no-go, residual, or obstruction is attempt evidence, not completion.
+
+## Accepted Baseline
+Work starts from accepted release `v0.160.0`, framework commit `1b00c3a` (branch `research/p230-exact-mass-regulator-rung` off updated `origin/main`, which contains the P227 closure `2072648`). Source audited at this commit (with landed-conditional status noted per the PR #77 review): `AGENTS.md`; `.agents/skills/physics-erdos-loop/SKILL.md` and its `references/governance.md` and `references/oracles.md`; `.agents/skills/research-pr-harvest/SKILL.md`; `tools/agent-memory/skills/shared_agent-memory-usage/SKILL.md` (CLI sections); `governance/releases/current.yaml` (207 accepted claims); `governance/claims.yaml` entries `C-GRV-001`, `C-GOR-001/002`, `C-STG-001/002`, `C-WLN-001..003`, `C-LOR-001/002`, `C-GW-001..010`; issue #76 body; issues #9 and #12 including all four comments each; `src/substrate_framework/scalar_induced_newton.py` and `src/substrate_framework/covariant_sine_gordon_action.py` (both landed conditional unpromoted APIs; the PR #14 and PR #25 harvests promoted no claims); `src/substrate_framework/einstein_scalar.py` docstring conventions; `src/substrate_framework/governance.py` (proposal schema). Chronology and memory prose are not authority; every reused fact was verified at source.
+
+## Constraints and Invariants
+Conventions are exactly the landed conditional `scalar_induced_newton` ones (accepted C-GRV-001 supplies only the conditional dimensional and additive-baseline ledger): `D_E = -nabla_E^2 + xi R_E + m^2`, boundaryless Gilkey-Seeley-DeWitt weights `a_2 = ((1/6 - xi) R_E - m^2)` under the `(4*pi)^-2` prefactor, one-real-scalar determinant weight `1/2`, and the Euclidean Einstein-Hilbert matching factor `16*pi`. The mass is retained exactly: no expansion of `exp(-tau*m^2)` inside the regulated proper-time integral. Target-blindness is a tested invariant: no observed `G`, `M_Pl`, or benchmark value may appear; the cutoff stays a declared formal scale; the power-subtracted scheme requires an explicit `renormalization_scale` argument (regulator non-defaulting, mirroring the accepted module). No new fitted constant. Permitted imports: `sympy` (including `expint`/`E1` and Bessel `K` closed forms), `scipy` quadrature in tests only, framework `exact_symbolic`, `scalar_induced_newton`, and the declared composition slot `covariant_sine_gordon_action` (`m^2 -> V''(phi_bg)`). Write boundary: `src/substrate_framework/scalar_one_loop_mass.py`, its `__init__` exports, `tests/test_scalar_one_loop_mass.py`, `proposals/P230-exact-mass-regulator-rung/`, and this record. Author-does-not-merge: open a PR naming #76 with `Advances #76`; a distinct reviewer/owner harvests and merges.
+
+## Decomposition
+1. [x] Recall and source verification (authority, #76 gates, #9 no-go, #12 ladder and PR #13/#25 handoffs, accepted rung conventions).
+2. [x] Candidate and selection-criteria preregistration in `proposals/P230-exact-mass-regulator-rung/proposal.yaml` (validated WORKFLOW VALID at `1b00c3a`).
+3. [x] Coordination comment on #76 (branch, proposal id, claim ids after collision search, slice, write surfaces, comparator-blinding point).
+4. [x] Importable implementation of the closed forms for the tau^-2 and tau^-3 classes under all three regulators, with exact symbolic APIs.
+5. [x] Verifier and sensitivity audit: quadrature cross-check of every closed form, massless-sharp reduction to the accepted `s*Lambda^2`, small-z asymptotic recovery, mutations (xi sign, prefactor, special-function branch, unknown regulator, non-defaulted scale), and scheme-spread ledger.
+6. [x] Framework-fit and downstream replay (`scripts/validate.sh --full`: 2235 passed, ALL REPOSITORY WORKFLOW CHECKS PASS; `git diff --check` clean; GitNexus re-indexed at current commit, impact LOW, detect-changes maps only the new module and `__init__` exports; generated AGENTS.md injection from `gitnexus analyze` reverted per AGENTS_START_HERE) (`scripts/validate.sh` boundary appropriate to the diff; `git diff --check` separately).
+7. [~] Harvest PR advancing #76 opened as #77 (issue-first, `Advances #76`, author does not merge). Independent harvest review at head `04f26f2`: CHANGES REQUIRED (three blocking findings, all verified independently and repaired in attempt 0002 — vacuum double-count, zeta sign semantics, authority wording). Repaired head pushed; re-review requested; merge authority remains with the distinct reviewer.
+
+## Candidate Preregistration and Selection Criteria
+Selection criteria frozen before any comparison value is computed: (1) convention compatibility with the accepted rung APIs; (2) closed-form exactness in standard special functions with no fitted constants; (3) exact-mass integrity inside the regulated integral; (4) mutation sensitivity; (5) reuse value for the later cutoff-identification and renormalization-condition rungs; (6) regulator explicitness (scheme dependence stays visible).
+
+- Candidate A (sharp proper-time, exact mass): regulated integral `integral_{1/Lambda^2}^infty tau^-2 exp(-m^2 tau) dtau = Lambda^2*(exp(-z) - z*E1(z))`, `z = m^2/Lambda^2`. Directly discharges the PR #13 load-bearing finite-mass factor.
+- Candidate B (smooth essential-singularity weight `exp(-1/(Lambda^2 tau))`, exact mass): `integral_0^infty tau^-2 exp(-m^2 tau - 1/(Lambda^2 tau)) dtau = 2*Lambda^2*sqrt(z)*BesselK_1(2*sqrt(z))`. One convergent integral family for all weights; no hard step.
+- Candidate C (power-divergence-subtracted zeta/Mellin finite part with declared scale `mu`): `m^2*(ln(m^2/mu^2) + gamma_E - 1)`. Exhibits the logarithmic-running alternative in which no `Lambda^2` term survives.
+All three are retained as parallel schemes in the module (the rung's deliverable is the comparison itself, so the selection is "which schemes to expose", not "which one wins"); empirical comparators may not select among them.
+
+## Attempts
+Attempts are append-only and individually reproducible; each row names the diagnosed mechanism and the next materially different attempt.
+
+| Attempt | Candidate or repair | Artifact and command | Verdict | Mechanism | Next attempt |
+| --- | --- | --- | --- | --- | --- |
+| (pending) |  |  |  |  |  |
+
+## Validation
+Validation covers the actual objective, verifier sensitivity, limits, conventions, and dependency replay, not merely an exit code. Targeted oracle at the repaired head: `PYTHONPATH=src .venv/bin/python -m pytest tests/test_scalar_one_loop_mass.py -q` = 25 passed (5.84 s), including the review-driven additions: the mass-resummed determinant-integrand oracle, the d I_3/d m^2 = -I_2 derivative-identity oracle in all three schemes, the double-count rejection mutation, and both zeta sign counterexamples with undecidable and positive branches. Earlier 20/20 boundary at the first head (5.20 s). Full boundary: `bash scripts/validate.sh --full` = 2235 passed in 309.16 s, `ALL REPOSITORY WORKFLOW CHECKS PASS (full pytest suite)`; `git diff --check` clean in a separate invocation. GitNexus: index refreshed at the working commit; `impact leading_scalar_newton_shift_coefficient` = LOW risk, single new direct caller (`exact_mass_inverse_newton_shift`); `detect-changes` maps only `src/substrate_framework/scalar_one_loop_mass.py` (new) and `__init__.py` `__all__`/imports; zero affected execution flows. The `gitnexus analyze` run auto-appended a tracked-instruction block to `AGENTS.md`; it was reverted per AGENTS_START_HERE section 3 and not committed.
+
+## Debt Ledger
+Every new assumption, import, parameter, residual, broken consumer, or narrative inconsistency is recorded here and discharged; this table must be empty at close.
+
+| Debt | Introduced by | Why it is real | Discharge artifact | Status |
+| --- | --- | --- | --- | --- |
+| (none yet) |  |  |  |  |

memory/vantasner/proposals/P230-exact-mass-regulator-rung.md

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+---
+description: P230 exact-mass one-loop proper-time coefficients with preregistered regulator comparison, the next Route 1 rung toward the #76 emergent-gravity goal
+author: prime-agent
+created: '2026-08-18T00:00:00Z'
+updated: '2026-08-18T00:00:00Z'
+tags:
+- substrate-framework
+- campaign-proposal
+- route1-induced-gravity
+- issue-76
+category: proposals
+confidence: exploratory
+status: active
+---
+
+## Question and Positive Deliverable
+The campaign asks for the exact closed-form one-loop proper-time coefficients of the accepted Route 1 fluctuation operator `D_E = -nabla_E^2 + xi R_E + m^2` when the mass is retained exactly, compared across preregistered regulators, as the next rung of the #76 parameter-closed emergent-gravity goal. The positive deliverable is an importable target-blind module plus tests; a no-go or obstruction is attempt evidence and does not complete it.
+
+## Base Release and Provenance
+The base is accepted release `v0.160.0` at framework commit `1b00c3a`, branch `research/p230-exact-mass-regulator-rung`. The manifest `proposals/P230-exact-mass-regulator-rung/proposal.yaml` records the source inventory: the two landed conditional (unpromoted) prior-work modules (`scalar_induced_newton.py` from the PR #14 harvest `a562568`; `covariant_sine_gordon_action.py` from the PR #25 harvest `65e4a7c`; both harvests promoted no claims) and the two already-imported literature convention sources (Vassilevich `hep-th/0306138` eqs (2.2)/(4.27); Visser `gr-qc/0204062` eqs (8)-(21)).
+
+## Invariants, Conventions, and Allowed Imports
+The frozen invariants are the accepted operator and scheme conventions, exact-mass integrity, target-blindness with a declared formal cutoff, no new fitted constants, unchanged accepted claims/releases/docs until independent adjudication, and non-self-merge. Allowed imports are SymPy exact algebra with special-function closed forms, SciPy quadrature in tests only, and the framework modules `scalar_induced_newton`, `covariant_sine_gordon_action` (mass slot `m^2 = V''(phi_bg)`), and `exact_symbolic`.
+
+## Candidate Preregistration
+Three schemes are preregistered in the manifest: (A) sharp proper-time lower cutoff with the exact-mass factor `Lambda^2*(exp(-z) - z*E1(z))`; (B) smooth essential-singularity proper-time weight with `2*Lambda^2*sqrt(z)*BesselK_1(2*sqrt(z))`; (C) power-divergence-subtracted zeta finite part `m^2*(ln(m^2/mu^2) + gamma_E - 1)`. The rung exposes all three rather than selecting one, because its deliverable is the exact scheme comparison that the later renormalization-condition rung must cite.
+
+## Selection Criteria and Blinding
+The frozen structural criteria are convention compatibility, closed-form exactness, exact-mass integrity, mutation sensitivity, reuse value, and regulator explicitness. Empirical gravitational comparators stay blinded for this rung and until a later renormalization-condition rung freezes scheme, scale, and cutoff identification; the landed conditional coefficient `s = N*(1-6*xi)/(12*pi)` is a framework ledger result, not a comparator.
+
+## Proposed Claim Delta
+Provisional claim identifiers after a repository-wide collision search (zero usages of the `C-IGR` family in governance, campaigns, proposals, memory, src, tests, and docs): `C-IGR-001` for the sharp exact-mass closed forms and their massless/asymptotic reductions; `C-IGR-002` for the smooth-weight closed forms; `C-IGR-003` for the power-subtracted finite-part forms and the exact scheme-spread ledger. Dependencies: the accepted `C-GRV-001` ledger structure. No `supersedes` is used before acceptance.
+
+## Implementation and Oracle Plan
+Implementation lands in `src/substrate_framework/scalar_one_loop_mass.py` with `__init__` exports and `tests/test_scalar_one_loop_mass.py`. Oracles: SymPy closed forms derived (not asserted) from the regulated integrals; SciPy `quad` cross-checks on convergent representations; sharp-massless exact reduction to `leading_scalar_newton_shift_coefficient`; small-`z` series recovery of the accepted leading term; mutations for xi sign, prefactor, special-function branch, unknown regulator, and non-defaulted renormalization scale. Replay: repository validation at the final unchanged boundary and `git diff --check` in a separate invocation.
+
+## Attempts
+Attempts live in `proposals/P230-exact-mass-regulator-rung/attempts/` and are append-only.
+
+## Continuation
+Issue #76 remains the canonical open goal; this rung advances it and proposes no closure.
+
+## Review Boundary (append-only, 2026-08-18)
+The independent harvest review of PR #77 at head `04f26f2` required changes: the vacuum-density API double-counted the mass (resummed `I_3` composed with the unresummed `-m^2` weight; exact difference `-(N/2)(4*pi)^-2*m^2*I_2`), the shift `sign` field did not describe the zeta-scheme value (counterexample `value=(EulerGamma-1)/(12*pi)<0` with `sign=+1`), and the dependency authority was overstated (the two prior-work modules are landed conditional APIs, not accepted claims). All three findings were verified independently and repaired in attempt 0002; the repair keeps the integral atoms, composes only `I_3` in the vacuum value, splits `curvature_weight_sign` from `value_sign`, and carries the conditional-provenance wording. The failed formulas remain in PR history at `04f26f2`.

proposals/P230-exact-mass-regulator-rung/attempts/0001/manifest.yaml

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+id: attempt-0001
+campaign: P230
+candidate: A+B+C parallel scheme exposure (preregistered in proposal.yaml)
+command: >
+  PYTHONPATH=src .venv/bin/python -m pytest tests/test_scalar_one_loop_mass.py -q
+working_directory: /home/dan/substrate-framework
+base_release: v0.160.0
+source_commit: 1b00c3a
+elapsed_seconds: 5.20
+exit_code: 0
+verdict: pass
+diagnosed_layer: none (first rung attempt succeeded)
+notes: >
+  20/20 targeted tests. Exact oracles: sharp tail-integral uniqueness
+  (derivative identity + exponential decay bound with E1 <= exp(-x)/x),
+  sharp tau^-3 integration-by-parts identity, smooth Bessel family
+  differential recurrence dJ_p/dz = -J_{p-1} with boundary limits J_2(0+)=1
+  and J_3(0+)=1, zeta power-subtraction limits, massless sharp reduction to
+  the accepted s*Lambda^2, small-z series 1 + z(ln z + gamma - 1),
+  40-digit mpmath quadrature corroboration at z in {0.1, 1.0, 2.5},
+  mutation sensitivity (prefactor, Ei-vs-E1 branch, Bessel order, xi sign
+  across 1/6, unknown regulator, defaulted scales, negative mass,
+  non-integer field count, undecidable xi), and target-blindness scan.
+  PR #13 bridge: F(1) = 0.1484955068 reproduces the review's named factor.
+full_boundary: >
+  bash scripts/validate.sh --full -> 2235 passed in 309.16s;
+  ALL REPOSITORY WORKFLOW CHECKS PASS (full pytest suite);
+  git diff --check clean (separate invocation, rc=0).

proposals/P230-exact-mass-regulator-rung/attempts/0002/manifest.yaml

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+id: attempt-0002
+campaign: P230
+candidate: repair of attempt-0001 after independent harvest review (PR #77 review, changes required at 04f26f2)
+command: >
+  PYTHONPATH=src .venv/bin/python -m pytest tests/test_scalar_one_loop_mass.py -q
+working_directory: /home/dan/substrate-framework
+base_release: v0.160.0
+source_commit: 04f26f2 (reviewed head) -> repaired head
+elapsed_seconds: 5.84
+exit_code: 0
+verdict: repaired (25/25)
+diagnosed_layer: implementation/concept boundary in the two composed public APIs; the integral atoms were correct
+review_findings_and_verifications:
+  F1_vacuum_double_count: >
+    VERIFIED INDEPENDENTLY. exact_mass_vacuum_density_shift composed the
+    mass-resummed tau^-3 integral with the unresummed -m^2 weight
+    (value used I_3 + m^2*I_2). The exact factored determinant gives
+    -(N/2)*(4*pi)^-2*I_3 only; the difference is -(N/2)*(4*pi)^-2*m^2*I_2,
+    nonzero for m^2>0 (symbolically: m2*(exp(-m2*tau0)/tau0 - m2*E1(m2*tau0))).
+    The massless regression could not catch it because the spurious term
+    vanishes at m=0. Repair: value composes only I_3; new oracle
+    test_derivative_identity_links_the_two_integral_classes proves
+    d I_3/d m^2 = -I_2 exactly in all three schemes (the exact bridge
+    showing the -m^2 weight is the first-order remnant of the retained
+    exponential); mutation test requires the double-counted composition to
+    differ by the spurious term and that the term is nonzero for m^2>0.
+  F2_zeta_sign_semantics: >
+    VERIFIED INDEPENDENTLY. The sign field described only 1/6-xi while the
+    zeta I_2 changes sign with m^2/mu^2: counterexample N=1, xi=0,
+    m^2=mu^2=1 returned value=(EulerGamma-1)/(12*pi)<0 with sign=+1, and
+    the m^2=0 branch returned 0 with sign=+1. Repair: split into
+    curvature_weight_sign (decidable sign of 1/6-xi, ValueError when
+    undecidable, landed-module precedent) and value_sign (decidable sign of
+    the full value, None when symbolic inputs leave it undecidable). Both
+    reviewer counterexamples plus a large-mass positive branch and a
+    symbolic undecidable branch are now tests.
+  F3_authority_overstatement: >
+    VERIFIED INDEPENDENTLY. scalar_induced_newton (PR #14) and
+    covariant_sine_gordon_action (PR #25) are landed conditional
+    (unpromoted) APIs; both harvest handoffs state 'Claims promoted: none';
+    accepted C-GRV-001 supplies only the conditional dimensional and
+    additive-baseline ledger. Repair: module docstring now carries an
+    explicit authority note; 'accepted module/scheme factor/weights'
+    wording replaced by 'landed conditional' provenance in the module, the
+    proposal manifest source inventory, both memory records, and the PR
+    body; all new public symbols remain explicitly unpromoted conditional
+    infrastructure linked to open goal #76.
+next_materially_different_route: none required for the atoms; advance to the tau^-1 class (curvature-squared sector) after merge adjudication