Pith Number

pith:ENIL4O4W

pith:2026:ENIL4O4WY7DNWJYAUL5IQLKOXU

not attested not anchored not stored refs pending

Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

Ayaka Shimizu, Yoshiro Yaguchi

arxiv:2601.02323 v2 · 2026-01-05 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENIL4O4WY7DNWJYAUL5IQLKOXU}

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	2026-06-02T02:04:49.849012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2350be3b96c7c6db2700a2fa882d4ebd2052540c652e8b838bbdf6b08459f9fc

Aliases

arxiv: 2601.02323 · arxiv_version: 2601.02323v2 · doi: 10.48550/arxiv.2601.02323 · pith_short_12: ENIL4O4WY7DN · pith_short_16: ENIL4O4WY7DNWJYA · pith_short_8: ENIL4O4W

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/ENIL4O4WY7DNWJYAUL5IQLKOXU \
  | 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: 2350be3b96c7c6db2700a2fa882d4ebd2052540c652e8b838bbdf6b08459f9fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f8634c43af88d38972294fe05916b4c1833fccbaa43664f7df2cc4b042cf589",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2026-01-05T18:14:58Z",
    "title_canon_sha256": "f0a38e5581d9a4511e74e9e7ac407062f1e3e5d02643ce94f28b0734f92b78f1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.02323",
    "kind": "arxiv",
    "version": 2
  }
}