Pith Number

pith:XSN2N3I7

pith:2003:XSN2N3I7CHUGPCPAZCGQ32G4SK

not attested not anchored not stored refs pending

Virtual strings and their cobordisms

Vladimir Turaev

arxiv:math/0311185 v5 · 2003-11-12 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XSN2N3I7CHUGPCPAZCGQ32G4SK}

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	2026-05-18T01:05:28.527908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc9ba6ed1f11e86789e0c88d0de8dc9286ac4bf382061b59bc8d7b32e10b0a76

Aliases

arxiv: math/0311185 · arxiv_version: math/0311185v5 · doi: 10.48550/arxiv.math/0311185 · pith_short_12: XSN2N3I7CHUG · pith_short_16: XSN2N3I7CHUGPCPA · pith_short_8: XSN2N3I7

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/XSN2N3I7CHUGPCPAZCGQ32G4SK \
  | 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: bc9ba6ed1f11e86789e0c88d0de8dc9286ac4bf382061b59bc8d7b32e10b0a76

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a5f1efbe276258dce934f2c74553b7c3fe53c722208114fba7677d1c26caeb2",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2003-11-12T09:30:28Z",
    "title_canon_sha256": "b2b86ca07418c3aa0e1420ea6c91509252805ef071d6ae3a90a228191f973445"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0311185",
    "kind": "arxiv",
    "version": 5
  }
}