Pith Number

pith:R3LFTNKL

pith:2021:R3LFTNKLH4HII5AKJGJQJ4WBKI

not attested not anchored not stored refs pending

Alexander polynomials of ribbon knots and virtual knots

Sheng Bai

arxiv:2103.07128 v3 · 2021-03-12 · math.GT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R3LFTNKLH4HII5AKJGJQJ4WBKI}

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.

Cited by

1 paper in Pith

A Fast, Strong, Topologically Meaningful and Fun Knot Invariant

Receipt and verification

First computed	2026-05-21T01:05:01.346272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8ed659b54b3f0e84740a499304f2c152316e00de9e01aef19bb08a8c5ca97c27

Aliases

arxiv: 2103.07128 · arxiv_version: 2103.07128v3 · doi: 10.48550/arxiv.2103.07128 · pith_short_12: R3LFTNKLH4HI · pith_short_16: R3LFTNKLH4HII5AK · pith_short_8: R3LFTNKL

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/R3LFTNKLH4HII5AKJGJQJ4WBKI \
  | 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: 8ed659b54b3f0e84740a499304f2c152316e00de9e01aef19bb08a8c5ca97c27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ab7b5c6045258a5045dc06310791be15d63ce179bb8fe34a917a10a6c3a8dc6f",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-03-12T07:57:59Z",
    "title_canon_sha256": "85da5e6ed7fb83e1c8adbdbc13f96c17fc1443291aed9215e921a2446f5011f8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.07128",
    "kind": "arxiv",
    "version": 3
  }
}