Pith Number

pith:G4JMNP63

pith:2013:G4JMNP63RSJGETOBSPBDKINCNT

not attested not anchored not stored refs pending

Various stabilities of the Alexander polynomials of knots and links

Kunio Murasugi, Mikami Hirasawa

arxiv:1307.1578 v1 · 2013-07-05 · 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{G4JMNP63RSJGETOBSPBDKINCNT}

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	2026-05-18T03:19:12.492655Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3712c6bfdb8c92624dc193c23521a26cef424f9a31a745fcbd913be112284473

Aliases

arxiv: 1307.1578 · arxiv_version: 1307.1578v1 · doi: 10.48550/arxiv.1307.1578 · pith_short_12: G4JMNP63RSJG · pith_short_16: G4JMNP63RSJGETOB · pith_short_8: G4JMNP63

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/G4JMNP63RSJGETOBSPBDKINCNT \
  | 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: 3712c6bfdb8c92624dc193c23521a26cef424f9a31a745fcbd913be112284473

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b384eb748d40716f382c670349d4d2253a2323fafaa7743488fee682f9918505",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-07-05T10:54:07Z",
    "title_canon_sha256": "bd7d2146668393fc7aa1c3ae525ae5df19ba1fd14a2c993477851d915df7dbfa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1578",
    "kind": "arxiv",
    "version": 1
  }
}