Pith Number

pith:DWXIJDBD

pith:2015:DWXIJDBDOWP7DQQKSS4MRJPG74

not attested not anchored not stored refs pending

Inside the clustering window for random linear equations

Michael Molloy, Pu Gao

arxiv:1512.06657 v2 · 2015-12-18 · cs.CC · math.CO · 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{DWXIJDBDOWP7DQQKSS4MRJPG74}

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	2026-05-18T00:51:34.200003Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1dae848c23759ff1c20a94b8c8a5e6ff02aefe42082d14914eb8ec25325071fa

Aliases

arxiv: 1512.06657 · arxiv_version: 1512.06657v2 · doi: 10.48550/arxiv.1512.06657 · pith_short_12: DWXIJDBDOWP7 · pith_short_16: DWXIJDBDOWP7DQQK · pith_short_8: DWXIJDBD

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/DWXIJDBDOWP7DQQKSS4MRJPG74 \
  | 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: 1dae848c23759ff1c20a94b8c8a5e6ff02aefe42082d14914eb8ec25325071fa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b3a23ad1a95334c00a1668dc4c8598462f1bb3689f534039b84d6f760d20c112",
    "cross_cats_sorted": [
      "math.CO",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2015-12-18T03:16:39Z",
    "title_canon_sha256": "0831109681aaeaaa0c7f6282aa1c9cd18eaeba01434fc160e1594c918e9782b0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.06657",
    "kind": "arxiv",
    "version": 2
  }
}