Pith Number record

pith:RE7YA4NU

pith:2016:RE7YA4NUEPAVNSZTI7K5XFZRCI

Protocol content-addressed Pith receipt schema 1.0

Author: not author-attested
Timestamp: not externally anchored
Storage: storage not verified
References: references not resolved

On an analogue of the Markov equation for exceptional collections of length 4

Louis de Thanhoffer de Volcsey, Michel Van den Bergh

Source: arxiv:1607.04246 v1 · Submitted 2016-07-14 · License http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Categories: math.AG

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Record completeness checklist

Each row is a typed event attached to this Pith Number. Done rows show their third-party proof. Open rows have an inline form so you can complete them without leaving this page.

1 Anchor canonical hash to Bitcoin via OpenTimestamps open

Stamps the canonical SHA-256 (893f8071b423c156cb3347d5...) across three calendars. Confirms instantly. Calendars upgrade to a Bitcoin-block proof in a few hours.

2 Mirror to Internet Archive (Wayback Machine) open

Submits the paper URL to the Internet Archive and records the resulting Wayback capture URL plus timestamp. Pith does not host the paper.

3 Claim authorship open

Identity-backed. The same flow as the paper page. Sign in with ORCID, Apple, X, or email magic-link; if your ORCID is on the arXiv author list the attestation is one-click and shows ORCID verified.

4 Sign a citation pointing at this record open

Records a signed citation. Pick a relationship (supports, refutes, extends, uses_method, depends_on, replaces, compares, cites). Pith signs the assertion server-side.

Relationship

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5 Submit replication, falsification, or formal bridge open

Public record of a replication attempt, formal bridge (Lean / Coq), or falsification. Held for moderation. Not peer review; a typed annotation.

Result class

Evidence URL (http(s))

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Claims

Inbound citations

1 paper in Pith references this work.

Three-periodic helices on elliptic curves and their associated regular algebras

arXiv:2604.21900 · ref [18]

Receipt

First computed	2026-05-18T01:11:03.771813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`, fingerprint `8d4b5ee74e4693bc…`) · public key
Signature value	`xm1Yl+kmFjpPpVhS3zUr8RsAZFJ7jBhtoq4gCOjghGR6mB2SUURMYB/3fC30kWvZ9CXQrMrQt6KKMBdsru2sAQ==`
Schema	pith-number/v1.0

Canonical hash

893f8071b423c156cb3347d5db973112307400d13f5a8190d00db5f02bf5cef3

Aliases

Kind	Value
arxiv	`1607.04246`
arxiv_version	`1607.04246v1`
doi	`10.48550/arxiv.1607.04246`

Agent API

Same address serves humans and agents. Add an Accept header to get the JSON-LD payload at the resolver URL itself.

Resolver JSON Graph JSON Events JSON Schema Signing key Resolve alias

Verify this Pith Number yourself

Three shell lines recompute the canonical hash. If the hash you compute matches the one shown above, the record is intact end-to-end.

curl -sH 'Accept: application/ld+json' https://pith.science/pith/RE7YA4NUEPAVNSZTI7K5XFZRCI \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 893f8071b423c156cb3347d5db973112307400d13f5a8190d00db5f02bf5cef3

Verify the Pith Ed25519 signature against the published public key:

curl -s https://pith.science/pith-signing-key.json | jq -r .public_key_b64 \
  | base64 -d > /tmp/pith_pub.bin
python3 -c "
from cryptography.hazmat.primitives.asymmetric.ed25519 import Ed25519PublicKey
import base64
pub = Ed25519PublicKey.from_public_bytes(open('/tmp/pith_pub.bin','rb').read())
sig = base64.b64decode('xm1Yl+kmFjpPpVhS3zUr8RsAZFJ7jBhtoq4gCOjghGR6mB2SUURMYB/3fC30kWvZ9CXQrMrQt6KKMBdsru2sAQ==')
digest = bytes.fromhex('893f8071b423c156cb3347d5db973112307400d13f5a8190d00db5f02bf5cef3')
pub.verify(sig, digest)
print('signature OK')"

Show canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "555f061b664a9e875461992c0a221d23e110c17f9ccf29d4cb1332d1d03799a1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-07-14T18:53:56Z",
    "title_canon_sha256": "cdad06d19540addbd0604a3acf60f1bdc22862fa567826066a5e8acda13b31a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1607.04246",
    "kind": "arxiv",
    "version": 1
  }
}