Pith Number

pith:W4G7EUL3

pith:2007:W4G7EUL3LE7YFUS5JDWYMIBTUR

not attested not anchored not stored refs pending

A Simple Proof of Sharkovsky's Theorem Rerevisited

Bau-Sen Du

arxiv:0711.3892 v9 · 2007-11-25 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4G7EUL3LE7YFUS5JDWYMIBTUR}

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	2026-05-18T02:19:08.837217Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b70df2517b593f82d25d48ed862033a469f8cfdcfc78154e2ccaf08cf9e04ef9

Aliases

arxiv: 0711.3892 · arxiv_version: 0711.3892v9 · doi: 10.48550/arxiv.0711.3892 · pith_short_12: W4G7EUL3LE7Y · pith_short_16: W4G7EUL3LE7YFUS5 · pith_short_8: W4G7EUL3

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/W4G7EUL3LE7YFUS5JDWYMIBTUR \
  | 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: b70df2517b593f82d25d48ed862033a469f8cfdcfc78154e2ccaf08cf9e04ef9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ee7206a1151d40d688a7948b69b5af7c5fd29c7c2292ca0137c0660b2d0be27",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2007-11-25T10:34:29Z",
    "title_canon_sha256": "88bec430bc5fb26cd23ae528637f3d9cb06c791b4ed4c69b04890da9e56658be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.3892",
    "kind": "arxiv",
    "version": 9
  }
}