Pith Number

pith:VZQUT3UQ

pith:2011:VZQUT3UQADBGJXYSQ5QJEVGZB6

not attested not anchored not stored refs pending

Fixed Price of Groups and Percolation

Russell Lyons

arxiv:1109.5418 v1 · 2011-09-25 · math.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZQUT3UQADBGJXYSQ5QJEVGZB6}

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	2026-05-18T00:06:21.231701Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae6149ee9000c264df1287609254d90f8ca6453b8e63a59b29a8490c16f740e0

Aliases

arxiv: 1109.5418 · arxiv_version: 1109.5418v1 · doi: 10.48550/arxiv.1109.5418 · pith_short_12: VZQUT3UQADBG · pith_short_16: VZQUT3UQADBGJXYS · pith_short_8: VZQUT3UQ

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/VZQUT3UQADBGJXYSQ5QJEVGZB6 \
  | 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: ae6149ee9000c264df1287609254d90f8ca6453b8e63a59b29a8490c16f740e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96f4a8a38db62d6c2f4b1b94855f984b89c4b70131f388b2e0a0c48e49478618",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-09-25T23:55:18Z",
    "title_canon_sha256": "d4659a66fd60e932b10f6edfe56d2be95eb74360edf84a255fdac9a61d3968f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5418",
    "kind": "arxiv",
    "version": 1
  }
}