Pith Number

pith:YTILNPCI

pith:2014:YTILNPCIIKX6VACETFJKQOJD3U

not attested not anchored not stored refs pending

Surface pole bracket polynomials of virtual knots and twisted knots

Naoko Kamada

arxiv:1401.1569 v1 · 2014-01-08 · 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{YTILNPCIIKX6VACETFJKQOJD3U}

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	2026-05-18T03:02:58.576340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4d0b6bc4842afea80449952a83923dd1882f5522050f5ec3e182a2a53a209fb

Aliases

arxiv: 1401.1569 · arxiv_version: 1401.1569v1 · doi: 10.48550/arxiv.1401.1569 · pith_short_12: YTILNPCIIKX6 · pith_short_16: YTILNPCIIKX6VACE · pith_short_8: YTILNPCI

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/YTILNPCIIKX6VACETFJKQOJD3U \
  | 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: c4d0b6bc4842afea80449952a83923dd1882f5522050f5ec3e182a2a53a209fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86dcb75ca0dcac87f822cbf1cb39e46dee261db41d5a2cd699f0f2db9e0e765a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2014-01-08T03:01:09Z",
    "title_canon_sha256": "297f0cecfe90b95524927008e6041a5ae9cd395b4f4473ed5f3804e56cfae759"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1401.1569",
    "kind": "arxiv",
    "version": 1
  }
}