Pith Number

pith:6EL4ZI4Q

pith:2007:6EL4ZI4Q4A7ITM2SYZ5ICATI6L

not attested not anchored not stored refs pending

Stochastic Completeness of Graphs

Radoslaw K. Wojciechowski

arxiv:0712.1570 v2 · 2007-12-10 · math.SP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6EL4ZI4Q4A7ITM2SYZ5ICATI6L}

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	2026-07-04T15:06:10.404544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f117cca390e03e89b352c67a810268f2d3f56afbe563d6ddd79c892b661ba74f

Aliases

arxiv: 0712.1570 · arxiv_version: 0712.1570v2 · doi: 10.48550/arxiv.0712.1570 · pith_short_12: 6EL4ZI4Q4A7I · pith_short_16: 6EL4ZI4Q4A7ITM2S · pith_short_8: 6EL4ZI4Q

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/6EL4ZI4Q4A7ITM2SYZ5ICATI6L \
  | 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: f117cca390e03e89b352c67a810268f2d3f56afbe563d6ddd79c892b661ba74f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5f378236898b2aacd1875802737933dea495d5cfbc426984519baba7826bd0c4",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "",
    "primary_cat": "math.SP",
    "submitted_at": "2007-12-10T19:14:08Z",
    "title_canon_sha256": "1021873dd4b55f08bba9e133b981dc49b846de47051245f4f7ad1fb208eb206e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0712.1570",
    "kind": "arxiv",
    "version": 2
  }
}