Pith Number

pith:LPPC6EML

pith:2005:LPPC6EMLDJGTTG2VS2AQPQWVLF

not attested not anchored not stored refs pending

Crosscap number two knots in $S^3$ with (1,1) decompositions

Enrique Ram\'irez-Losada, Luis G. Valdez-S\'anchez

arxiv:math/0511005 v1 · 2005-10-31 · 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{LPPC6EMLDJGTTG2VS2AQPQWVLF}

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	2026-05-18T01:08:50.809760Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bde2f118b1a4d399b55968107c2d559714a61c166e3df7d7c6035b6c2bf75c0

Aliases

arxiv: math/0511005 · arxiv_version: math/0511005v1 · doi: 10.48550/arxiv.math/0511005 · pith_short_12: LPPC6EMLDJGT · pith_short_16: LPPC6EMLDJGTTG2V · pith_short_8: LPPC6EML

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/LPPC6EMLDJGTTG2VS2AQPQWVLF \
  | 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: 5bde2f118b1a4d399b55968107c2d559714a61c166e3df7d7c6035b6c2bf75c0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5025a18682b7bdb07adc2a091eb8992b3c56cac605c80c1068d72c7566f13fe",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2005-10-31T23:58:52Z",
    "title_canon_sha256": "573554b79349ee79da7f5f454406af4c2b8827cdb6d61152899e5c5f884dfcdd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0511005",
    "kind": "arxiv",
    "version": 1
  }
}