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Pith Number record

pith:GS7JQ5BQ

pith:2014:GS7JQ5BQ2MU2QN4F77WKZRHASH
Protocol content-addressed Pith receipt schema 1.0
Author
not author-attested
Timestamp
not externally anchored
Storage
storage not verified
References
references not resolved

Flat strips, Bowen-Margulis measures, and mixing of the geodesic flow for rank one CAT(0) spaces

Russell Ricks

Source: arxiv:1410.3921 v2 · Submitted 2014-10-15 · License http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Categories: math.DS · math.DG · math.GT

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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 (34be987430d329a83785ffec...) across three calendars. Confirms instantly. Calendars upgrade to a Bitcoin-block proof in a few hours.
Free. No account. Anyone can re-stamp; each stamp is an independent calendar receipt.
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.
Free, anonymous, third-party preservation.
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.
Returns you right back here after sign-in.
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.
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Held for moderation. Sign in to confirm immediately.
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.
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Held for moderation before it appears as confirmed.

Claims

Inbound citations

1 paper in Pith references this work.

Finiteness of Bowen-Margulis-Sullivan Measure for Gromov-Patterson-Sullivan Systems
arXiv:2604.03982 · ref [18]

Receipt

First computed 2026-05-18T00:33:32.950781Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05, fingerprint 8d4b5ee74e4693bc…) · public key
Signature value 39OICiD76r5Jn0ghpoTJ9qIpbcBKmLJ2sbbaj861S1ZC71YNTk+DYEsIhYlhsdoe6YjMVwM7f6FTHLkSwNqzCw==
Schema pith-number/v1.0

Canonical hash

34be987430d329a83785ffecacc4e091ee1eb334b19f3b2dd3042f5b38b13f78

Aliases

Kind Value
arxiv 1410.3921
arxiv_version 1410.3921v2
doi 10.48550/arxiv.1410.3921

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/GS7JQ5BQ2MU2QN4F77WKZRHASH \
  | 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: 34be987430d329a83785ffecacc4e091ee1eb334b19f3b2dd3042f5b38b13f78

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('39OICiD76r5Jn0ghpoTJ9qIpbcBKmLJ2sbbaj861S1ZC71YNTk+DYEsIhYlhsdoe6YjMVwM7f6FTHLkSwNqzCw==')
digest = bytes.fromhex('34be987430d329a83785ffecacc4e091ee1eb334b19f3b2dd3042f5b38b13f78')
pub.verify(sig, digest)
print('signature OK')"
Show canonical record JSON 
{
  "metadata": {
    "abstract_canon_sha256": "7fcee0d9ba708fa12924c7a632ba59ff3fd30dd56e262ff1540268a41143dbac",
    "cross_cats_sorted": [
      "math.DG",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2014-10-15T04:03:04Z",
    "title_canon_sha256": "ed2c1fc7f0d5ce5eec3af2293415768ce534579df09d7ca2d71ce292bd2b9fcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.3921",
    "kind": "arxiv",
    "version": 2
  }
}