Pith Number

pith:XSARTFFS

pith:2011:XSARTFFS5ISRKFUPWWC22RVGSG

not attested not anchored not stored refs pending

An integral expression of the first non-trivial one-cocycle of the space of long knots in R^3

Keiichi Sakai

arxiv:1104.0073 v1 · 2011-04-01 · math.GT · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XSARTFFS5ISRKFUPWWC22RVGSG}

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	2026-05-18T04:25:12.506324Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc811994b2ea2515168fb585ad46a691b188a958ac738ac4b1aa7a107efbbab9

Aliases

arxiv: 1104.0073 · arxiv_version: 1104.0073v1 · doi: 10.48550/arxiv.1104.0073 · pith_short_12: XSARTFFS5ISR · pith_short_16: XSARTFFS5ISRKFUP · pith_short_8: XSARTFFS

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/XSARTFFS5ISRKFUPWWC22RVGSG \
  | 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: bc811994b2ea2515168fb585ad46a691b188a958ac738ac4b1aa7a107efbbab9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3978eed22b5cf9f5281656259f4142785169c6b323fe1ce610185c7e1587fcbb",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-04-01T03:20:02Z",
    "title_canon_sha256": "70987b642d3defc322d9213bf0caa2c5b22f174458f6f14d9491835beca1da9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.0073",
    "kind": "arxiv",
    "version": 1
  }
}