Pith Number

pith:2U3WQLIK

pith:2015:2U3WQLIK47ON46Z5IC5X3MQE3T

not attested not anchored not stored refs pending

Explicit Expanding Expanders

Asaf Valadarsky, Michael Dinitz, Michael Schapira

arxiv:1507.01196 v1 · 2015-07-05 · cs.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2U3WQLIK47ON46Z5IC5X3MQE3T}

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	2026-05-18T01:37:17.765551Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d537682d0ae7dcde7b3d40bb7db204dce85d9c2bd21e452072548e6e41799751

Aliases

arxiv: 1507.01196 · arxiv_version: 1507.01196v1 · doi: 10.48550/arxiv.1507.01196 · pith_short_12: 2U3WQLIK47ON · pith_short_16: 2U3WQLIK47ON46Z5 · pith_short_8: 2U3WQLIK

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/2U3WQLIK47ON46Z5IC5X3MQE3T \
  | 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: d537682d0ae7dcde7b3d40bb7db204dce85d9c2bd21e452072548e6e41799751

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa81273466f5ec8651627292ceb2cf2bbce905334af81a816cce4fbbab6e5130",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2015-07-05T11:22:45Z",
    "title_canon_sha256": "5b01e6e8bd08257d3230a2ba5dbec73ca2db7e6946081fd4a8c278c6073ee216"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.01196",
    "kind": "arxiv",
    "version": 1
  }
}