Pith Number

pith:X5Z3FFA3

pith:2015:X5Z3FFA3WPYMXAEKQZIEQV4VO2

not attested not anchored not stored refs pending

Knot concordances and alternating knots

Charles Livingston, Raphael Zentner, Stefan Friedl

arxiv:1512.08414 v1 · 2015-12-28 · 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{X5Z3FFA3WPYMXAEKQZIEQV4VO2}

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	2026-05-18T00:39:57.038008Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf73b2941bb3f0cb808a8650485795769079e491088a28ef0ecd4b1942e03a10

Aliases

arxiv: 1512.08414 · arxiv_version: 1512.08414v1 · doi: 10.48550/arxiv.1512.08414 · pith_short_12: X5Z3FFA3WPYM · pith_short_16: X5Z3FFA3WPYMXAEK · pith_short_8: X5Z3FFA3

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/X5Z3FFA3WPYMXAEKQZIEQV4VO2 \
  | 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: bf73b2941bb3f0cb808a8650485795769079e491088a28ef0ecd4b1942e03a10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b980fce44961b2f537e44e8a9511ef44dd58ec91c78f39c122af3048d2b9ecbb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-12-28T13:59:24Z",
    "title_canon_sha256": "e7cf192427397ea47745ec7484d72f3927f5adedac7af63184010313eb139a12"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08414",
    "kind": "arxiv",
    "version": 1
  }
}