Pith Number

pith:SSO6WB57

pith:2011:SSO6WB572OQDGYNDAXR5JCKD62

not attested not anchored not stored refs pending

Markov Theorem For Free Links

Hang Wang, Vassily Olegovich Manturov

arxiv:1112.4061 v2 · 2011-12-17 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SSO6WB572OQDGYNDAXR5JCKD62}

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	2026-05-18T03:54:15.886031Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

949deb07bfd3a03361a305e3d48943f69c586d3b0a80250aac7e2b46aa73aab9

Aliases

arxiv: 1112.4061 · arxiv_version: 1112.4061v2 · doi: 10.48550/arxiv.1112.4061 · pith_short_12: SSO6WB572OQD · pith_short_16: SSO6WB572OQDGYND · pith_short_8: SSO6WB57

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/SSO6WB572OQDGYNDAXR5JCKD62 \
  | 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: 949deb07bfd3a03361a305e3d48943f69c586d3b0a80250aac7e2b46aa73aab9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a856a87c80e7cf47627e04363a08035f9ccfef2b9db65319f4aac7c56a003203",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-12-17T15:01:37Z",
    "title_canon_sha256": "a1bd0e8e3f684749424b15766f5dd4e0c3316dd7250b1d3978ce259f7eca6f64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.4061",
    "kind": "arxiv",
    "version": 2
  }
}