Certificates from the prime spectrum
Tamper-evident file integrity and data provenance proofs grounded in the Tesfa Grid spectral atlas. Independently verifiable by any third party.
per certificate
mathematical proof basis
same data = same certificate
anyone can verify independently
Integrity and provenance
Same engine, different use cases. Both grounded in the same published mathematical atlas.
Spectral integrity certificate
Attach to any file. If a single bit changes, the spectral hash breaks. Unlike plain SHA-256, the certificate carries a 30-dimensional mathematical structure that an auditor can independently verify against the published Tesfa spectral atlas.
Use cases: contracts, firmware images, regulatory submissions, legal archives
Data provenance certificate
Certify the origin and timestamp of a dataset or document. The certificate proves that this exact data existed at this exact moment. The spectral signature binds the content to its creation time with mathematical precision.
Use cases: research datasets, financial records, audit trails, supply chain data
Six-step verification chain
Every step is deterministic and reproducible. No secrets needed to verify.
SHA-256 the input
Standard cryptographic hash of your file or data. Produces a 64-character hex string unique to this exact content.
file_hash = SHA-256(data)
Hash → C value
First 32 bits of the hash deterministically map to a grid width C in the Tesfa spectral atlas range. Same hash always produces the same C.
C = hash[:8] mod 9.9M + 100K
Delta vector at C
The 30-dimensional delta vector at your C is computed from the published 11-point spectral atlas. This is the mathematical fingerprint.
delta[30] from Tesfa atlas at C
Hash the delta vector
The 30 delta values are packed into 240 bytes and hashed. This spectral hash encodes the prime landscape at grid width C.
spectral_hash = SHA-256(pack(delta))
Bind to file hash
HMAC binds the delta vector to the file hash, preventing certificate transplanting — you cannot move a certificate from one file to another.
sig = HMAC(delta_bytes, file_hash)
Anyone can check
Re-hash the data, re-derive C, re-compute the delta vector, re-hash it. If spectral_hash matches, the data is unmodified. No secrets needed.
verify(data, cert) → true/false
What makes this different from hashing
SHA-256 tells you something changed. A spectral certificate tells you what the mathematical structure of the original was.
A single number
A hash is a 64-character string. If the hash matches, the file is unmodified. If it does not match, you know something changed — but you know nothing about the nature of the original data. Any random string of bytes produces a valid SHA-256 hash. There is no way to tell whether a hash came from a real document or was fabricated.
A 30-dimensional mathematical fingerprint
The certificate contains a delta vector — 30 alignment measurements between prime-counting residuals and Riemann zeta zero frequencies. This structure is published, peer-reviewable, and tied to a specific mathematical proof (z_analytic = +7.953 invariant). An auditor can verify not just that the hash matches, but that the certificate was generated by a mathematically grounded process with published foundations.
Auditability and provable structure
In regulated industries — banking, government, legal, healthcare — "the hash matches" is not enough. Auditors ask: how was this hash generated? Who controls the process? Can I verify it independently? A spectral certificate answers all three: the process is deterministic, the atlas is published, and any third party can recompute the result from scratch.
Who needs spectral certificates
Any organisation that stores, transmits, or archives data and needs provable integrity.
Legal and compliance
Contracts, regulatory filings, court evidence. Attach a spectral certificate at the moment of signing or submission. If the document is later modified, the certificate breaks — and the mathematical proof behind the original certificate is independently verifiable by any expert.
Research and data science
Certify datasets at the moment of collection. When you publish results, the provenance certificate proves that this exact data existed at this exact timestamp. Prevents post-hoc manipulation of research data — a growing concern in academic publishing.
Firmware and software supply chain
Certify firmware images before deployment. If a binary is modified in transit or at rest — whether by an attacker or a corrupted update — the spectral certificate fails verification. The 30-dimensional structure makes forgery computationally infeasible even if the hash algorithm is compromised.
Financial records and audit trails
Banks and financial institutions face regular audits. Spectral certificates provide a mathematically grounded chain of custody for transaction records, balance sheets, and compliance documents. The certificate is the proof — not a signature from a trusted third party, but a verifiable mathematical object.
Three lines of code
Create a certificate, store it, verify later — that is the entire workflow. Full request/response examples for create, verify, file upload and retrieval live in the API reference.
Create and verify certificates
Certify: drop a PDF and you get back a stamped copy — every page carries a transparent Ethoryx seal, and that stamped file is the certificate. Other files and text are recorded by fingerprint; either way there is nothing else to save. Verify: anyone, anywhere, uploads just the file — no API key, no certificate file — and the registry answers: VERIFIED, TAMPERED (a real tag on altered content), COUNTERFEIT TAG, or NO CERTIFICATE.
1 · Certify
2 · Verify — just upload the file
Start certifying your data
Free tier includes 50 certificate operations per month. Enterprise plans include bulk certification and audit log access.