Pith Number

pith:BY43VOKD

pith:2015:BY43VOKDXLOGFFCWMB6W7ABF6M

not attested not anchored not stored refs pending

Detection in the stochastic block model with multiple clusters: proof of the achievability conjectures, acyclic BP, and the information-computation gap

Colin Sandon, Emmanuel Abbe

arxiv:1512.09080 v4 · 2015-12-30 · math.PR · cs.CC · cs.IT · cs.LG · cs.SI · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BY43VOKDXLOGFFCWMB6W7ABF6M}

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.

Cited by

1 paper in Pith

Detectability of minority communities in networks

Receipt and verification

First computed	2026-05-18T01:04:37.661193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0e39bab943badc629456607d6f8025f32c4d8d7697c081b378ebe30c0762b503

Aliases

arxiv: 1512.09080 · arxiv_version: 1512.09080v4 · doi: 10.48550/arxiv.1512.09080 · pith_short_12: BY43VOKDXLOG · pith_short_16: BY43VOKDXLOGFFCW · pith_short_8: BY43VOKD

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/BY43VOKDXLOGFFCWMB6W7ABF6M \
  | 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: 0e39bab943badc629456607d6f8025f32c4d8d7697c081b378ebe30c0762b503

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01981eeacd724a2c1594edce02b59fc8522bea41c9c82cd15746cd73975009fb",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.IT",
      "cs.LG",
      "cs.SI",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-30T19:49:28Z",
    "title_canon_sha256": "f7ca50cebb4a60cdca190bc10c55979cab6f4da0f92b21520bdcf90dc3f04bce"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.09080",
    "kind": "arxiv",
    "version": 4
  }
}