Pith Number

pith:OFJ33M4E

pith:2016:OFJ33M4EKRHGQQ2ZMN6HN7NPRR

not attested not anchored not stored refs pending

Circle-valued Morse theory for frame spun knots and surface-links

Andrei Pajitnov, Hisaaki Endo

arxiv:1605.04532 v1 · 2016-05-15 · 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{OFJ33M4EKRHGQQ2ZMN6HN7NPRR}

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	2026-05-18T00:30:49.049428Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7153bdb384544e684359637c76fdaf8c50525654506b756a23e3172c511826e0

Aliases

arxiv: 1605.04532 · arxiv_version: 1605.04532v1 · doi: 10.48550/arxiv.1605.04532 · pith_short_12: OFJ33M4EKRHG · pith_short_16: OFJ33M4EKRHGQQ2Z · pith_short_8: OFJ33M4E

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/OFJ33M4EKRHGQQ2ZMN6HN7NPRR \
  | 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: 7153bdb384544e684359637c76fdaf8c50525654506b756a23e3172c511826e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57764ac5d543a6b9f865c3ca31440501cb716a42b63c9f45ad161ef8e98ffc28",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-05-15T12:17:44Z",
    "title_canon_sha256": "2f0fb333babefaf01cb378c5e9d3646f42fb4578768bb333e576efc9d45b82cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.04532",
    "kind": "arxiv",
    "version": 1
  }
}