Pith Number

pith:3NPXEYRF

pith:2012:3NPXEYRFL65LG2MRLJ7EESSM7X

not attested not anchored not stored refs pending

Computing closed essential surfaces in knot complements

Alexander Coward, Benjamin A. Burton, Stephan Tillmann

arxiv:1212.1531 v1 · 2012-12-07 · math.GT · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3NPXEYRFL65LG2MRLJ7EESSM7X}

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	2026-05-18T03:15:57.605433Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e

Aliases

arxiv: 1212.1531 · arxiv_version: 1212.1531v1 · doi: 10.48550/arxiv.1212.1531 · pith_short_12: 3NPXEYRFL65L · pith_short_16: 3NPXEYRFL65LG2MR · pith_short_8: 3NPXEYRF

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/3NPXEYRFL65LG2MRLJ7EESSM7X \
  | 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: db5f7262255fbab369915a7e424a4cfdfc7592e26b3fa3a167bb0d1032904a0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7868ae034aa4e745b8f54eb9119f2a6978529f7e94dba62bcd6ad1579cc6be14",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-12-07T05:48:05Z",
    "title_canon_sha256": "02c79a8b67385ff56c08c14b139b34beec23770792ec5006724008f0989a036e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1531",
    "kind": "arxiv",
    "version": 1
  }
}