ZEH/LTB research-workflow reference

Working title: Spatial Backreaction and Light-Cone Observables in LTB Cosmology: An Identifiability Analysis.

This package formalizes the investigation; it does not settle it. ZEH-Q-03 (non-identifiability) is an open conjecture with no theorem artifact. A green suite proves the executed fragment replays and the open status is preserved — never that the LTB theorem is proved.

Code: github.com/PithomLabs/phys-lib/gr/ltb

Question

Given an admissible LTB class and a fixed past-light-cone distance observation, what does it determine about present-day Buchert backreaction Q_D(t0) on a specified comoving domain? Backreaction is identifiable iff Q[D_A*] = {Q_D^M(t0)} is a singleton under the stated class, foliation, domain, and normalization.

What is executed

• dM/dr for M(r) = r^3/2 via DIFFERENTIATE-001, replayed, bound to the hand golden 3r^2/2 through a stored EQ relation and theorem conclusion gate.
• EXPR-CANON-001 on the EdS theta = H + 2H construction, replayed.
• Go rational corroboration (pointwise, not symbolic proof) of the EdS cone identity and the series coefficients below.

What is represented only

Spatial averaging and the volume measure (no integration primitive was added — growth gate), sigma vanishing beyond its factored structure, the off-cone extension, the Q_2 functional, and all claim statuses.

Hand derivations (independently re-derived, not copied)

Conventions: M(r) = r^3/2 exactly (never r^{3/2}); area radius R = D_A on the central cone; R'(t0,0) = 1, t0 = 2/3 as declared constitution.

1. Target series. (1+z)^-1/2 = 1 - z/2 + 3z^2/8 - 5z^3/16 + ... (binomial). Numerator 2[1 - ...] = z - 3z^2/4 + 5z^3/8 - .... Dividing by (1+z) via (1 - z + z^2 - ...) gives D_A*(z) = z - 7z^2/4 + 19z^3/8 + .... The 19/8 coefficient corrects the earlier 23/8 slip caught by the composition check.
2. EdS vertex profile. Z0(r) = (1-r/2)^-2 = 1 + r + 3r^2/4 + r^3/2 + ..., so z(r) = r + 3r^2/4 + ...: z_2 = 3/4 (data-fixed under the central normalization). The r^3 coefficient 1/2 verifies the beta = 0 case of the candidate recursion z_3 = 1/2 + 2*beta/3; the 2*beta/3 slope itself stays a candidate and is not used as a golden.
3. Cone identity. With u = 1-r/2, V0 = r/u, Q0 = 1/u, Rc0 = r*u^2, P0 = u^2: LHS 2*V0*Q0 = 2r/u^2; RHS 3r^2/Rc0 - r^3*P0/Rc0^2 = 3r/u^2 - r/u^2 = 2r/u^2. Holds identically for u != 0.
4. Gauge derivative. d/dr[r^3/2] = 3r^2/2 (monomial power rule).

Claim register

• ZEH-Q-01: literature claim requiring verification (MHE background).
• ZEH-Q-02: candidate construction, incomplete (O1, O2, O3 open).
• ZEH-Q-03: open conjecture (O1, O3, O4, O5, O6, O7 open). No function-counting inference: metric freedom does not imply Q_D variance until Q_2[h] != 0 is established under the exact constraint. CheckClaimPromotion only rejects a proved status with missing or out-of-inventory evidence; inventory membership does not establish that a derivation proves the promoted claim.
• ZEH-Q-04: deferred branch, out of this slice.

Stored EdS vertex coefficients

VertexCoeffs maps series order to rational artifacts (1->1, 2->3/4, 3->1/2) for z(r) = Z0(r)-1. These are finite-order baseline values with independent mechanical recomputation — not the general candidate recursion z_3 = 1/2 + 2*beta/3, analytic existence, or any ZEH-Q claim.

Variable-identity note

The production H is an ephemeral symbol: its encoded identity is its display string, with no ParameterID. Tests assert both operands match the same intended stored representation (byte-identical encodings) — syntactic sameness, not bound-parameter identity and not physical meaning. A synthetic bound-symbol control shows same-display/different-ParameterID symbols are distinguished; it does not confer bound-parameter identity on the production artifact.

Layout

fixture.go (Build + Verify), claim.go (metadata consistency check), manifest.json (strict machine metadata), manifest_test.go (schema + status pins), protocol/derivation_test.go (execution, goldens, anti-goldens, provenance, coverage, determinism).