Pith Number

pith:32KEPZGQ

pith:2009:32KEPZGQFHCCIPKBOHRNXLHNDF

not attested not anchored not stored refs pending

Stabilizing Four-Torsion in Classical Knot Concordance

Charles Livingston, Swatee Naik

arxiv:0908.0005 v1 · 2009-07-31 · 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{32KEPZGQFHCCIPKBOHRNXLHNDF}

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	2026-05-18T03:12:09.345198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

de9447e4d029c4243d4171e2dbaced1970d6005b0109a9f3585bfd349e7c1f41

Aliases

arxiv: 0908.0005 · arxiv_version: 0908.0005v1 · doi: 10.48550/arxiv.0908.0005 · pith_short_12: 32KEPZGQFHCC · pith_short_16: 32KEPZGQFHCCIPKB · pith_short_8: 32KEPZGQ

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/32KEPZGQFHCCIPKBOHRNXLHNDF \
  | 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: de9447e4d029c4243d4171e2dbaced1970d6005b0109a9f3585bfd349e7c1f41

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d8f288c6ca1f8a561875945e480c5833949a0b996f0ae5162c9ba694d8ee918f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-07-31T20:37:20Z",
    "title_canon_sha256": "e8b7ff9723b8572acd4b8528775e6009a95171bbdaedc1e9ab5d3cb2073e4905"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0908.0005",
    "kind": "arxiv",
    "version": 1
  }
}