What does this research mean for the field?

Failed supernovae occur when a star's Planck Shell reaches the ~10 km bounce radius (yielding a critical mass of 3.14 M☉), predicting that their occurrence tracks stellar merger history rather than progenitor mass. Novelty: ClaimNovelty.CONTRADICTORY. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

Evaluate the mechanism of failed core-collapse supernovae within the Photonic Universe Hypothesis by replacing the flawed surface throughput criterion with a geometric structural threshold.

August 23, 2026Open Access

PUH Theorem 341 (A Structural Criterion for Failed Supernovae) — The Throughput Criterion Fails by Forty Orders, but Requiring the Shell to Reach the Bounce Radius Gives M_crit = 3.14 M☉; and the Framework Predicts Failed Supernovae Track MERGER HISTORY, Not Progenitor Mass

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Evaluate the mechanism of failed core-collapse supernovae within the Photonic Universe Hypothesis by replacing the flawed surface throughput criterion with a geometric structural threshold.
Calculated energy throughput ratios by comparing empirical surface flux models against typical core-collapse supernova power outputs (1.0e45 W over 10 s).
Derived the structural cutoff radius r_shell(M) = (2GM/c^2) * X / (X - 1) setting X ≈ 14 against the canonical 10 km nuclear-stiffening bounce radius.
Demonstrated that the previous throughput criterion fails by forty orders of magnitude (power ratio 6.9e-40), requiring an unphysical core mass of 5.0e19 solar masses.
Established an unfitted structural threshold critical mass of 3.14 solar masses for the 10 km bounce radius, placing the remnant within the astrophysical mass gap between neutron stars and black holes.
Predicted that failed supernovae correlate with stellar merger history and binary amalgamation rather than isolated progenitor mass alone.

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Implication

Theoretical modeling demonstrates that Planck shell structural expansion dictates failed supernova thresholds at 3.14 solar masses, suggesting star merger history drives direct collapse.

Cite This Study

Brian Martell (2026) studied this question.

synapsesocial.com/papers/6a8aae337677a34114446f93 https://doi.org/10.5281/zenodo.22050969

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Implication

Theoretical modeling demonstrates that Planck shell structural expansion dictates failed supernova thresholds at 3.14 solar masses, suggesting star merger history drives direct collapse.

PUH Theorem 341 (A Structural Criterion for Failed Supernovae) — The Throughput Criterion Fails by Forty Orders, but Requiring the Shell to Reach the Bounce Radius Gives M_crit = 3.14 M☉; and the Framework Predicts Failed Supernovae Track MERGER HISTORY, Not Progenitor Mass

Key Points

Discussion

Implication

Cite This Study

PUH Theorem 341 (A Structural Criterion for Failed Supernovae) — The Throughput Criterion Fails by Forty Orders, but Requiring the Shell to Reach the Bounce Radius Gives M_crit = 3.14 M☉; and the Framework Predicts Failed Supernovae Track MERGER HISTORY, Not Progenitor Mass

Key Points

Discussion

Implication

Cite This Study

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