Pith Number

pith:67FDT62V

pith:2015:67FDT62VPRJ54Y66FYNXZN3EVE

not attested not anchored not stored refs pending

On the Morse-Novikov number for 2-knots

Andrei Pajitnov, Hisaaki Endo

arxiv:1502.06352 v1 · 2015-02-23 · 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{67FDT62VPRJ54Y66FYNXZN3EVE}

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	2026-05-18T00:30:49.564052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7ca39fb557c53de63de2e1b7cb764a91651f9cf80bc9b7e891f9623e4a2191a

Aliases

arxiv: 1502.06352 · arxiv_version: 1502.06352v1 · doi: 10.48550/arxiv.1502.06352 · pith_short_12: 67FDT62VPRJ5 · pith_short_16: 67FDT62VPRJ54Y66 · pith_short_8: 67FDT62V

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/67FDT62VPRJ54Y66FYNXZN3EVE \
  | 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: f7ca39fb557c53de63de2e1b7cb764a91651f9cf80bc9b7e891f9623e4a2191a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "751131a62b7defec4ab6dc9c5f3c9c45bc3495a771e832ef3010bca919081bfb",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-02-23T09:05:02Z",
    "title_canon_sha256": "6ec4d0dcccd8241ffb3a02d684cf6f8bca35233602b79f50eca8faa87ab8a9a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.06352",
    "kind": "arxiv",
    "version": 1
  }
}