Pith Number

pith:4PAZO4IS

pith:2013:4PAZO4IS5EQZM7XQ4EGUPDHRNB

not attested not anchored not stored refs pending

The Three Loop Isotopy and Framed Isotopy Invariants of Virtual Knots

H. A. Dye, Micah W. Chrisman

arxiv:1309.2971 v1 · 2013-09-11 · 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{4PAZO4IS5EQZM7XQ4EGUPDHRNB}

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	2026-05-18T03:13:33.206616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3c1977112e921967ef0e10d478cf16871e5a512699aa23bf98e0d8b388b8540

Aliases

arxiv: 1309.2971 · arxiv_version: 1309.2971v1 · doi: 10.48550/arxiv.1309.2971 · pith_short_12: 4PAZO4IS5EQZ · pith_short_16: 4PAZO4IS5EQZM7XQ · pith_short_8: 4PAZO4IS

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/4PAZO4IS5EQZM7XQ4EGUPDHRNB \
  | 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: e3c1977112e921967ef0e10d478cf16871e5a512699aa23bf98e0d8b388b8540

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8171253fbc44ea6c47ca17b7dc98f44f2ac67ac767709b6e14d347b5d6afadd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-09-11T21:02:51Z",
    "title_canon_sha256": "05d53ade4aac33b92f48ced8c596690b4ca5fcf83d5083a676b432ffec84b78f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.2971",
    "kind": "arxiv",
    "version": 1
  }
}