Pith Number

pith:OKUO6JU3

pith:2013:OKUO6JU3D2II6ITMAAW5HVUW4J

not attested not anchored not stored refs pending

Phase transitions in Number Theory: from the Birthday Problem to Sidon Sets

Bartolo Luque, Ivan G. Torre, Lucas Lacasa

arxiv:1310.3817 v1 · 2013-10-12 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OKUO6JU3D2II6ITMAAW5HVUW4J}

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	2026-05-18T01:47:05.641720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

72a8ef269b1e908f226c002dd3d696e26d4f5cd43cf9836bb3f105f925b0a202

Aliases

arxiv: 1310.3817 · arxiv_version: 1310.3817v1 · doi: 10.48550/arxiv.1310.3817 · pith_short_12: OKUO6JU3D2II · pith_short_16: OKUO6JU3D2II6ITM · pith_short_8: OKUO6JU3

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/OKUO6JU3D2II6ITMAAW5HVUW4J \
  | 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: 72a8ef269b1e908f226c002dd3d696e26d4f5cd43cf9836bb3f105f925b0a202

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e1e1957a9918946f66a69d3f6bac1ea9deb3ae874539ba83a81d7898ff5f3251",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2013-10-12T12:21:46Z",
    "title_canon_sha256": "354769086c9d22e1efed860b301d26105d1e5f37607f6183dcec2d8c62e0b13e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.3817",
    "kind": "arxiv",
    "version": 1
  }
}