Pith Number

pith:3LRK5D4N

pith:2000:3LRK5D4NYYFV7MKN2XSMKQGNML

not attested not anchored not stored refs pending

The volume of hyperbolic alternating link complements

Marc Lackenby

arxiv:math/0012185 v2 · 2000-12-19 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3LRK5D4NYYFV7MKN2XSMKQGNML}

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	2026-07-04T14:34:59.403415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dae2ae8f8dc60b5fb14dd5e4c540cd62c0db7a01693ab3d907de497cce379bc4

Aliases

arxiv: math/0012185 · arxiv_version: math/0012185v2 · doi: 10.48550/arxiv.math/0012185 · pith_short_12: 3LRK5D4NYYFV · pith_short_16: 3LRK5D4NYYFV7MKN · pith_short_8: 3LRK5D4N

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/3LRK5D4NYYFV7MKN2XSMKQGNML \
  | 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: dae2ae8f8dc60b5fb14dd5e4c540cd62c0db7a01693ab3d907de497cce379bc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67ed5b28a53ba8eddcf3035e361dd3305298623cc35fa6c0bdcc9a69d6c41145",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2000-12-19T22:29:49Z",
    "title_canon_sha256": "b61d201a8910e1ff9c0124d63a3e546c401e72cba0f71ae5bd716677a263ed44"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0012185",
    "kind": "arxiv",
    "version": 2
  }
}