Pith Number

pith:D64XVZNJ

pith:2018:D64XVZNJNTMPV7FJ3JLL7JUS4U

not attested not anchored not stored refs pending

Winding number and Cutting number of Harmonic cycle

Woong Kook, Younng-Jin Kim

arxiv:1812.04930 v2 · 2018-12-12 · math.CO · math.AT · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D64XVZNJNTMPV7FJ3JLL7JUS4U}

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	2026-05-17T23:58:20.476182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1fb97ae5a96cd8fafca9da56bfa692e5387682f6244f0741a321cce513b9172c

Aliases

arxiv: 1812.04930 · arxiv_version: 1812.04930v2 · doi: 10.48550/arxiv.1812.04930 · pith_short_12: D64XVZNJNTMP · pith_short_16: D64XVZNJNTMPV7FJ · pith_short_8: D64XVZNJ

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/D64XVZNJNTMPV7FJ3JLL7JUS4U \
  | 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: 1fb97ae5a96cd8fafca9da56bfa692e5387682f6244f0741a321cce513b9172c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ce4a411803ed1b24c13006b791e8079273e8194b7a167ee2792897cf354f9b73",
    "cross_cats_sorted": [
      "math.AT",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-12-12T13:13:24Z",
    "title_canon_sha256": "2403706d06d2a755752840a1132c18a4dd615ddbbee8f9dc66224a836886c4d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.04930",
    "kind": "arxiv",
    "version": 2
  }
}