Pith Number

pith:KPXQ6RKN

pith:2012:KPXQ6RKNMLS5UIU3VVVKYKW56G

not attested not anchored not stored refs pending

A Brouwer fixed point theorem for graph endomorphisms

Oliver Knill

arxiv:1206.0782 v1 · 2012-06-04 · math.DS · cs.DM · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KPXQ6RKNMLS5UIU3VVVKYKW56G}

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	2026-05-18T03:54:16.357882Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

53ef0f454d62e5da229bad6aac2addf186cea8e88086e1c3a54589e4c826071a

Aliases

arxiv: 1206.0782 · arxiv_version: 1206.0782v1 · doi: 10.48550/arxiv.1206.0782 · pith_short_12: KPXQ6RKNMLS5 · pith_short_16: KPXQ6RKNMLS5UIU3 · pith_short_8: KPXQ6RKN

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/KPXQ6RKNMLS5UIU3VVVKYKW56G \
  | 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: 53ef0f454d62e5da229bad6aac2addf186cea8e88086e1c3a54589e4c826071a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b6e7dd02b18c9949d6767c6a47895ad6015557c146ac94dad16f9418583921ef",
    "cross_cats_sorted": [
      "cs.DM",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-06-04T22:13:51Z",
    "title_canon_sha256": "9db4bf94756ab3e4e6a3b784dca4cfe459dfaa8e77cbd6e677c3cacf9dc9889e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1206.0782",
    "kind": "arxiv",
    "version": 1
  }
}