Pith Number

pith:KNM65I45

pith:2010:KNM65I457TWQLC73SCFEG3IZZE

not attested not anchored not stored refs pending

Connected sum at infinity and Cantrell-Stallings hyperplane unknotting

Henry C. King, Jack S. Calcut, Laurent C. Siebenmann

arxiv:1010.2707 v1 · 2010-10-13 · 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{KNM65I457TWQLC73SCFEG3IZZE}

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	2026-05-18T04:39:19.803692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5359eea39dfced058bfb908a436d19c92f06e16d0772b6e14278660372902ca9

Aliases

arxiv: 1010.2707 · arxiv_version: 1010.2707v1 · doi: 10.48550/arxiv.1010.2707 · pith_short_12: KNM65I457TWQ · pith_short_16: KNM65I457TWQLC73 · pith_short_8: KNM65I45

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/KNM65I457TWQLC73SCFEG3IZZE \
  | 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: 5359eea39dfced058bfb908a436d19c92f06e16d0772b6e14278660372902ca9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d74ae13f90c240bb2b8bb36b134c7b17602c48c96f69cc887f827e2285304d69",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-10-13T17:13:37Z",
    "title_canon_sha256": "ccf4d4c54abf78ff96cd97c2433d3fca708076a442c6d06071d562a73b56d4e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2707",
    "kind": "arxiv",
    "version": 1
  }
}