Pith Number

pith:ZAQ6FBOU

pith:2003:ZAQ6FBOUSALIWHEFFQ2B3BLB2H

not attested not anchored not stored refs pending

Knot mutation: 4-genus of knots and algebraic concordance

Charles Livingston, Se-Goo Kim

arxiv:math/0310100 v1 · 2003-10-07 · 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{ZAQ6FBOUSALIWHEFFQ2B3BLB2H}

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	2026-05-18T04:28:08.464165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c821e285d490168b1c852c341d8561d1f9f127119866073cee283644ed39d767

Aliases

arxiv: math/0310100 · arxiv_version: math/0310100v1 · doi: 10.48550/arxiv.math/0310100 · pith_short_12: ZAQ6FBOUSALI · pith_short_16: ZAQ6FBOUSALIWHEF · pith_short_8: ZAQ6FBOU

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/ZAQ6FBOUSALIWHEFFQ2B3BLB2H \
  | 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: c821e285d490168b1c852c341d8561d1f9f127119866073cee283644ed39d767

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e70aaae98dab79791b925678cc6bc48c190a6f06941839528d9c29a4f2217ea",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-10-07T21:25:59Z",
    "title_canon_sha256": "767745a536b98f55fd1f823ac5d7d6cc9cae5efb21f2eeb3f5e594f70e55a1d1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0310100",
    "kind": "arxiv",
    "version": 1
  }
}