Astral Gate research program
Astral Gate is an auditable computational semiclassical-gravity and numerical-GR research program. Wormhole / backreaction physics is the ambitious application. We are not selling a gate.
Physical gate not established. No portal, warp drive, stable throat, or minimum mass has been demonstrated.
LIVE BOARD · 2026-10-09
October research update: scalar calculation repaired; independent trace agreement at r=6M under an empirical numerical allowance.
Three results stay separate. On 21 September this pipeline’s predeclared ε₁ oscillation passed on the unseen window ω ∈ [10.40, 10.90] only. Digitized published curves agree 12/12 at four radii, and the multi-radius chain remains MRX_R_INVALID. On 9 October the repaired scalar trace agrees with the stored PMR trace at r = 6M under a combined empirical allowance. None of these is an independently validated full stress tensor. The figures are the recorded research summaries, not a recalculation performed by this website.
What changed
The massless scalar subtraction was repaired and compared with the stored PMR trace at one radius, r = 6M. A September confirmation of the predeclared oscillation, a narrow published-curve comparison, and a target-exposed Hadamard derivation are now on the ledger as separate, narrower results.
Evidence
As of 2026-10-09. Scalar trace status TRACE_R6_NUMERICAL_PASS_UNDER_EMPIRICAL_BUDGET. Residual 1.5474844313788875×10⁻¹¹ against a combined empirical allowance 3.861830391164996×10⁻⁹. CNG confirmation is a 21 September narrow pass on ω ∈ [10.40, 10.90]. Published-curve agreement is 12/12 at four radii and does not repair the MRX_R_INVALID chain.
Limit
The allowance is empirical and dominated by the inherited PMR estimate. It is not a statistical confidence interval or a rigorous infinite-tail bound. Nine nearby scalar nodes support the derivative at r = 6M; they are not nine trace validations. No validated throat, backreaction solution, stability result, or engineering readiness.
Next step
Supported omitted-mode remainder control for the differentiated scalar sum; independent trace comparisons around r = 5.5M and 6.5M; then independent tensor components with consistent conventions, trace, conservation, and PMR comparison.
NAMED BLOCKERS FULL INDEPENDENT RSET FALSE · E NOT VALIDATED · WARD HOLD · INFINITE-SUPPORT INTEGRAL NOT PROVED · Mτ PAUSED · SIGN UNRESOLVED · GATE NO · NEXT Supported omitted-mode remainder control for the differentiated scalar sum; independent trace comparisons around r = 5.5M and 6.5M; then independent tensor components with consistent conventions, trace, conservation, and PMR comparison.
Latest research status · 2026-10-09
As of 9 October 2026 the live result is a repaired massless scalar trace at r=6M under a combined empirical allowance. That is not the 20 September discovery freeze, and it is not an independently validated stress tensor. The 21 September CNG window is a narrow pass for this pipeline only. The angular gate below is earlier instrument history.
How the failure was isolated
Observed high-ω failure
Precision / tolerance noise disfavored
ℓ-support isolated
Cancellation restored
ω=8 angular plateau demonstrated
Adaptive ℓ gate implemented
Prospective ω=7 validation
Sparse extension ω=10,12
Decaying high-ω tail
Analytic asymptotic-expectation audit
Dense CNG discovery scan
CNG independent confirmation
Global CNG structure
Finite-support self-cancellation
Infinite-support generalized integral
Independent HH benchmark reproduction
WHAT THIS IS
Literature permits growing CNG oscillations after local subtraction. A predeclared ε₁=37.5 oscillation is strongly present in the dense r=6M discovery scan. That is not confirmation. The confirmatory scan is running.
WHAT THIS IS NOT
Not numerical CNG confirmed. Not an HH RSET reproduction. Not Abel production. Not a traversable gate. Not a confirmed literature sign error.
Why B1 matters
B1 is calibration of the numerical instrument Astral Gate needs before testing unknown geometries. A successful B1 would not prove a gate; it would establish enough confidence in the quantum stress-tensor engine to begin broader benchmark work. Ultimately, that engine could become useful well outside Astral Gate for black-hole quantum physics, semiclassical backreaction, wormhole tests, and curved-spacetime QFT.
Branch G/B1 remains PARTIAL. As of 9 October 2026 the repaired massless scalar trace agrees with the stored PMR trace at r=6M under a combined empirical allowance. That is not an independently validated full stress tensor. A 21 September CNG window passed narrowly; global structure is not established. The mixed-time sign question remains EXTERNALLY REVIEWABLE, paused, and unconfirmed. Production sign is not flipped.
Paused literature / reproducibility lane
During independent validation of the B1 Schwarzschild Hartle–Hawking RSET engine, we isolated a potential overall-sign inconsistency in a displayed mixed-time derivative formula. Three independent internal derivations recover an overall PLUS mode contribution under our reading of the stated conventions, whereas the displayed TBO Eq. 18 / analogous ABOT Eq. 16 carries an overall MINUS. The result is externally reviewable, not confirmed. Public archaeology did not determine which sign was actually used in the private numerical implementation that generated the published tables. This lane is paused pending external clarification.
Modern-engine dependency graph
Radial and Hadamard layers have historical passes that October reassessed. The current comparison is a repaired scalar trace at one radius under an empirical allowance. A CNG window passed narrowly on 21 September and is not a global confirmation. Published curves agree 12/12 at four radii, and the full chain remains invalid. Ward and infinite-support Abel stay open. The displayed Mτ formula is paused and unconfirmed. This update does not flip the production sign.
TBO source
PASSRadial Green
PASSHP referee / zero mode
PASSm=6 Hadamard source, historical scope
PASS THEN · REASSESSEDSeptember stamps stay. October found a massless skip of nonzero tails and a wrong static-mode boundary coefficient.
Ψ⁺ η→1
PASSm=6 subtraction
PASS⟨φ²⟩ convergence
PASSSource-derived radial derivatives
PASSNested h derivative certification
PASSSynge reconstruction
PASSTrace
PASSPMR angular gate + sparse 10/12
ANGULAR_ACCEPTED TO ω=12Pointwise domain to ω=12 conditional on ℓ. Decaying tail not demonstrated. Not HH RSET. Not Abel.
PMR asymptotic-expectation audit
MIXED · GROWTH EXPECTED PRE-GIAfter F_sing, F_reg need not decay before GI. Closed analytic lane.
CNG discovery scan
STRONG EVIDENCEε₁=37.5 predeclared. 51/51 accepted. Not confirmation.
CNG confirmation window
NARROW PASS · 21 SEPThis pipeline, ω∈[10.40,10.90], ε₁ fixed. Not a global asymptotic claim.
Published HH curves
12/12 NARROWDigitized agreement at four radii. Full chain remains MRX_R_INVALID.
Hadamard e derivation
CANDIDATEa, b, e match. Target-exposed. E_VALIDATED = false.
Repaired scalar trace at r=6M
EMPIRICAL PASSCombined allowance only. Not every component. Not a tail bound.
Four-point RSET assembly DEV
HOLDMachinery exists. Promotion blocked. Production sign not flipped.
Ward identity
HOLDHoward four-point scoreboard
HOLDAbel / generalized-integral production
NOT VALIDATEDSynthetic referee PASS_DIAGNOSTIC. Limit order: Ω → ∞ first.
Displayed Mτ mixed-time formula
EXTERNALLY REVIEWABLE · PAUSEDNot confirmed. 3/3 PLUS internally. Archaeology unknown. Public pack READY.
Howard 35-row production grid
LOCKEDB1 reproduction
NOT CLAIMEDNovel AG throat / physical gate
NOT REACHEDValidated results
2026-10-09
After two implementation corrections, the massless Hartle–Hawking scalar at r=6M gives a trace residual 1.5474844313788875×10⁻¹¹ against the stored PMR trace. The scalar-only allowance does not cover that residual. A combined empirical allowance, dominated by the inherited PMR estimate, does. Status TRACE_R6_NUMERICAL_PASS_UNDER_EMPIRICAL_BUDGET. Figures are the editorial summary, not a rerun on this website.
2026-10-07
Sixteen recorded checks pass. c = d = 0. The derivation was target-exposed, not blind, and is not a second Christensen/AHS implementation. Reapplying the derived e left five stored tensors unchanged to roundoff. E_VALIDATED stays false.
2026-10-03
Reconciled 7 October. Component values at r=5.5, 6, 6.5, and 7 agree with digitized published Hartle–Hawking curves within stated tolerances. The full chain remains MRX_R_INVALID because r=5 failed tt n-convergence under analysis v1.0. A supplementary v1.1 pass does not replace that label.
2026-09-21
ω∈[10.40,10.90], 51/51 angular-accepted, ε₁=37.5 fixed. The accepted record reports C1–C6 PASS. C5 was corrected to joint-H1 source transfer plus a fresh target cubic. Accepted directional R² 0.9988049064965246 and 0.9985764043986991. A 9 October replay agrees at roundoff. Discovery D=FAIL and F=CRITERIA_GAP stay.
Nested-h closure · retained
That gate is closed and kept. It does not promote RSET. Qualifiers remain part of the PASS.
ξ_rad = 1.2
Coarse D(h) unavailable. Certification is h/2 → h/4 stability, source-derived modewise agreement, N/L spot referee, and mixed error budget. Not a measured three-level Richardson order. October 9: this PASS is the old implementation and tolerance, not the repaired scalar budget.
ξ_rad = 1.8
Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. Do not display negative formal p_est as a physics failure.
ξ_rad = 3.0
Both first and second nested-h refinements pass under the full gate combination then in force.
ξ_rad = 5.0
Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence.
| ξ_rad | h_refine_d1 | h_refine_d2 | Qualifier |
|---|---|---|---|
| 1.2 | PASS | PASS | Coarse D(h) unavailable. Certification is h/2 → h/4 stability, source-derived modewise agreement, N/L spot referee, and mixed error budget. Not a measured three-level Richardson order. October 9: this PASS is the old implementation and tolerance, not the repaired scalar budget. |
| 1.8 | PASS | PASS | Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. Do not display negative formal p_est as a physics failure. |
| 3.0 | PASS | PASS | Both first and second nested-h refinements pass under the full gate combination then in force. |
| 5.0 | PASS | PASS | Second-derivative successive differences are slightly non-monotonic at very small absolute scale. Interpreted as numerical floor / error-budget stability, not physical divergence. |