01PROVED
No negative spectrum.
The specified unperturbed mouth operator has no normalizable mode with negative squared frequency.
H ≥ 0
INDEPENDENT RESEARCH / EST. 2026
One mouth.
Three fields.
An exact result.
A closer look at the mathematics of a wormhole mouth. Explore its hidden positivity, a zero-energy resonance, and the questions they leave open.
01 / THE COUPLED MOUTH OPERATORℓ = 2 M = 10
near the mouth outward
gravitationalelectromagneticSchwinger
Manuscript · endorsement pending
One extended extremal mouth. A classical three-field model.
Study boundary01 / THE RESULTANALYTICAL · EXACT WITHIN THE MODEL
Hidden positivity,
made explicit.
Three coupled equations look complicated. An exact factorization exposes a simpler structure: the operator is a sum of nonnegative pieces.
THE CORE IDENTITY
ℓ ≥ 2 · fixed, finite M > 0
02PROVED
A unique threshold profile.
One independent bounded zero-energy resonance exists. Its nonzero tails make it non-normalizable.
H u0 = 0
03PROVED · CONDITIONAL
A delicate balance.
An arbitrarily weak compact attractive matrix perturbation binds a negative mode if it overlaps the resonance.
Hε = H − εB
Inside the model
The symmetrized fields obey H Y = k²Y, with H = −∂²x + V. The dimensionless radius is r > 1, the mouth radius is set to one, and L = ℓ(ℓ + 1).
M = m²S is the Schwinger screening parameter. It is not the black-hole mass or a fermion rest mass. The result uses the published extremal-mouth approximation and lowest-Landau-level matter response.
For the attraction theorem, B is bounded, compactly supported and positive semidefinite, with positive overlap ∫u0†Bu0 dx. Whether a physical correction has this form is a separate question.
Read the equations and proof02 / THE INTERACTIVE MODELCHANGE A PARAMETER. INSPECT THE RESULT.
The mathematics,
within reach.
Compare computed transmission with a threshold prediction, or examine the exact spatial resonance. Every plotted scattering point comes from a saved calculation.
NEUTRAL TRANSMITTED FLUX
89.728%
ℓ = 2 · M = 100 · k = 0.00001
10⁻⁵10 saved points per parameter pair0.3
near the mouthlog(r − 1)outward
Where the master flux goes
Neutral transmitted —Other transmitted —Neutral reflected —Other reflected —
Components of u0 / a at the selected radius
Y₁ · gravitational —Y₂ · electromagnetic —Y₃ · Schwinger —
Solid points: computed neutral transmission. Dashed line: threshold matching prediction, not a proved limit.
These quantities describe conserved classical master flux. They are not qubit fidelity or a teleportation success probability.
03 / THE RESEARCH RECORDMANUSCRIPTS, DATA & METHODS
Read it.
Question it.
A growing collection of results, with their assumptions and limitations attached. The first manuscript is ready to inspect.
PAPER01OCTOBER 2026
Manuscript · arXiv endorsement pending
Positive Factorization and a Zero-Energy Resonance of the Schwinger-Coupled Wormhole Mouth
Dmitry Kosarevsky · Independent Researcher
An exact positivity identity, a unique bounded threshold resonance, and a conditional weak-attraction binding theorem for a specified three-channel extremal-mouth operator.
Last status update: 22 October 2026. Endorsement requested; no final arXiv submission or external human peer review is recorded. The manuscript, derivation and saved data are public; the numerical solver source remains private. Detailed derivation · Website source
04 / THE NEXT QUESTIONSOPEN RESEARCH · NO RESULTS CLAIMED
A result opens
another question.
Further papers will follow substantive results. These are the directions being investigated, not a promised publication schedule.
NEXT RESEARCH TARGET
How fragile is the resonance?
Determine how a weak local correction changes the bound-state scale and transmission near zero frequency. The challenge is a controlled threshold theorem for coupled inverse-square tails.
OPEN DIRECTION
What changes between two mouths?
Understand which results survive in a complete finite-throat geometry, with the matching conditions and both asymptotic regions treated together.
OPEN DIRECTION
When does a field become a channel?
Establish physical quantum normalization, an encoding, and a receiver before interpreting classical master-field transmission as quantum information transfer.
THE BOUNDARY OF THE CLAIM
Ambitious questions.
Precise statements.
This work establishes properties of one classical extremal-mouth operator. A complete traversable wormhole, a physical quantum channel, and a teleportation prototype remain outside the established results.
The research used significant AI assistance in derivations, code, literature checks and drafting. Dmitry Kosarevsky is responsible for the manuscript; independent specialist scrutiny is welcome.
Discuss the research