Pith Number

pith:AX4O35YT

pith:2015:AX4O35YTSLUDQNFJCX3OJAVOH6

not attested not anchored not stored refs pending

Expanders via Local Edge Flips

Aditya Bhaskara, Lorenzo Orecchia, Silvio Lattanzi, Vahab Mirrokni, Zeyuan Allen-Zhu

arxiv:1510.07768 v1 · 2015-10-27 · cs.DS · cs.DC · cs.NI · 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{AX4O35YTSLUDQNFJCX3OJAVOH6}

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	2026-05-18T01:29:12.675763Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05f8edf71392e83834a915f6e482ae3fa01702ff36772c30b0178dd55fbbf92c

Aliases

arxiv: 1510.07768 · arxiv_version: 1510.07768v1 · doi: 10.48550/arxiv.1510.07768 · pith_short_12: AX4O35YTSLUD · pith_short_16: AX4O35YTSLUDQNFJ · pith_short_8: AX4O35YT

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/AX4O35YTSLUDQNFJCX3OJAVOH6 \
  | 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: 05f8edf71392e83834a915f6e482ae3fa01702ff36772c30b0178dd55fbbf92c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8378de8ebd3b500d8de086a90d3779a31ed9d5a6eef7e743533fc3089ed4eb58",
    "cross_cats_sorted": [
      "cs.DC",
      "cs.NI",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2015-10-27T04:13:17Z",
    "title_canon_sha256": "42f1d65b0f6e9f33cb1667aa0555e37f29476ec7d7d9547bc5eadbcf74173e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.07768",
    "kind": "arxiv",
    "version": 1
  }
}