Pith Number

pith:3HWHA7YA

pith:2015:3HWHA7YA2BHIJ5UECR5JJM76JC

not attested not anchored not stored refs pending

Residual periodicity on the Markoff surface

Solomon Vishkautsan

arxiv:1504.07099 v2 · 2015-04-27 · math.NT · math.AG · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3HWHA7YA2BHIJ5UECR5JJM76JC}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:15:38.780332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9ec707f00d04e84f684147a94b3fe48b5155bb071096023cba7e7bdfe36c1bb

Aliases

arxiv: 1504.07099 · arxiv_version: 1504.07099v2 · doi: 10.48550/arxiv.1504.07099 · pith_short_12: 3HWHA7YA2BHI · pith_short_16: 3HWHA7YA2BHIJ5UE · pith_short_8: 3HWHA7YA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3HWHA7YA2BHIJ5UECR5JJM76JC \
  | 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: d9ec707f00d04e84f684147a94b3fe48b5155bb071096023cba7e7bdfe36c1bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "83e73d7bb152049bdc0dc47208988714d2cb3cdf34ce1c3db3b3022d25a57e44",
    "cross_cats_sorted": [
      "math.AG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-04-27T14:09:57Z",
    "title_canon_sha256": "3c5d013f78891bdb4fedc59ea310cd0c66dac6d9f058d55f0251bdda1b6d95d0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.07099",
    "kind": "arxiv",
    "version": 2
  }
}