Pith Number

pith:O7LQSGON

pith:2016:O7LQSGONRDHXKUMIWRVCDCY2ZG

not attested not anchored not stored refs pending

Group-like expansions and invariants of string links

Hisatoshi Kodani

arxiv:1604.03213 v2 · 2016-04-12 · math.AT · 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{O7LQSGONRDHXKUMIWRVCDCY2ZG}

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	2026-05-18T01:10:19.881106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77d70919cd88cf755188b46a218b1ac99d5d9ffb98f2b506e493787e4cce1cba

Aliases

arxiv: 1604.03213 · arxiv_version: 1604.03213v2 · doi: 10.48550/arxiv.1604.03213 · pith_short_12: O7LQSGONRDHX · pith_short_16: O7LQSGONRDHXKUMI · pith_short_8: O7LQSGON

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/O7LQSGONRDHXKUMIWRVCDCY2ZG \
  | 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: 77d70919cd88cf755188b46a218b1ac99d5d9ffb98f2b506e493787e4cce1cba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5bc22ff24a7745e5bbc1428625f810b657bc6dee4bb9a979172766a2c31917f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2016-04-12T02:42:57Z",
    "title_canon_sha256": "73871d67b18bc6f06207a0e5b8c4f473b7883e61b4382a6f35eb1c5fe8e1f959"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.03213",
    "kind": "arxiv",
    "version": 2
  }
}