Pith Number

pith:J34ADX5O

pith:2015:J34ADX5O2SFBZPXHFGRUDTBKIY

not attested not anchored not stored refs pending

High-Girth Matrices and Polarization

Emmanuel Abbe, Yuval Wigderson

arxiv:1501.06528 v2 · 2015-01-26 · cs.IT · 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{J34ADX5O2SFBZPXHFGRUDTBKIY}

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	2026-05-18T02:27:56.738305Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ef801dfaed48a1cbee729a341cc2a4637491df05c917996cf22c6a28d61a7e3

Aliases

arxiv: 1501.06528 · arxiv_version: 1501.06528v2 · doi: 10.48550/arxiv.1501.06528 · pith_short_12: J34ADX5O2SFB · pith_short_16: J34ADX5O2SFBZPXH · pith_short_8: J34ADX5O

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/J34ADX5O2SFBZPXHFGRUDTBKIY \
  | 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: 4ef801dfaed48a1cbee729a341cc2a4637491df05c917996cf22c6a28d61a7e3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb72796a64381ea12481071ef06a5c43a72ee8dffb5e03f9370e386212c4477e",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2015-01-26T19:14:33Z",
    "title_canon_sha256": "bb7d6b42c2c5ae7f1e3cc98a4620e34a3c6186c7192d7eee7c8649a631f7695f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.06528",
    "kind": "arxiv",
    "version": 2
  }
}