Pith Number

pith:TAU2MLYN

pith:1999:TAU2MLYNZHJ7UNID2KRUR2FKEL

not attested not anchored not stored refs pending

On McMullen's and other inequalities for the Thurston norm of link complements

Brian S. Mangum, Oliver T. Dasbach

arxiv:math/9911172 v2 · 1999-11-23 · 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{TAU2MLYNZHJ7UNID2KRUR2FKEL}

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	2026-05-18T02:41:26.486950Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9829a62f0dc9d3fa3503d2a348e8aa22f3f4c90c47ae540824b34ed8b69c280a

Aliases

arxiv: math/9911172 · arxiv_version: math/9911172v2 · doi: 10.48550/arxiv.math/9911172 · pith_short_12: TAU2MLYNZHJ7 · pith_short_16: TAU2MLYNZHJ7UNID · pith_short_8: TAU2MLYN

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/TAU2MLYNZHJ7UNID2KRUR2FKEL \
  | 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: 9829a62f0dc9d3fa3503d2a348e8aa22f3f4c90c47ae540824b34ed8b69c280a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "530f5cefc29a149ff62fa15e0f9c8575f889c2bc1f26f0297cf232a1f273ddf7",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "1999-11-23T00:33:03Z",
    "title_canon_sha256": "98cf4e0fc0a5af1561f43cd717b495525357f549d6e028239cc5c069b7d81d09"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9911172",
    "kind": "arxiv",
    "version": 2
  }
}