Pith Number

pith:KHK3745H

pith:2010:KHK3745HPNRWKF7QDXFHPNWBTO

not attested not anchored not stored refs pending

Region crossing change is an unknotting operation

Ayaka Shimizu

arxiv:1011.6304 v4 · 2010-11-29 · 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{KHK3745HPNRWKF7QDXFHPNWBTO}

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	2026-05-18T03:02:07.710888Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51d5bff3a77b636517f01dca77b6c19bae24e49f00945444fa595d4dc95e865d

Aliases

arxiv: 1011.6304 · arxiv_version: 1011.6304v4 · doi: 10.48550/arxiv.1011.6304 · pith_short_12: KHK3745HPNRW · pith_short_16: KHK3745HPNRWKF7Q · pith_short_8: KHK3745H

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/KHK3745HPNRWKF7QDXFHPNWBTO \
  | 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: 51d5bff3a77b636517f01dca77b6c19bae24e49f00945444fa595d4dc95e865d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8f0cb71243edb76b08d21d2ca06b4ad5d40a0174b4a8268831e07b21bd23f02c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-11-29T17:45:14Z",
    "title_canon_sha256": "965b30eaa3f3dcc02d685ceb969372d71a0d47f662e324f6fe54d59a134f2775"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.6304",
    "kind": "arxiv",
    "version": 4
  }
}