Pith Number

pith:CHYJO2ZP

pith:2018:CHYJO2ZPCLBIU4DBMRVRXCNE63

not attested not anchored not stored refs pending

Generic uniqueness of expanders with vanishing relative entropy

Alix Deruelle, Felix Schulze

arxiv:1812.08504 v2 · 2018-12-20 · math.DG · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CHYJO2ZPCLBIU4DBMRVRXCNE63}

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	2026-07-05T00:57:43.637231Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

11f0976b2f12c28a7061646b1b89a4f6f12066da5e53cb9ff15573a8c6c5e507

Aliases

arxiv: 1812.08504 · arxiv_version: 1812.08504v2 · doi: 10.48550/arxiv.1812.08504 · pith_short_12: CHYJO2ZPCLBI · pith_short_16: CHYJO2ZPCLBIU4DB · pith_short_8: CHYJO2ZP

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/CHYJO2ZPCLBIU4DBMRVRXCNE63 \
  | 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: 11f0976b2f12c28a7061646b1b89a4f6f12066da5e53cb9ff15573a8c6c5e507

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbe3f88abc69243b4b9f23e24f517be9cc534c533969f04ac4dfcfbbb6c44791",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2018-12-20T12:00:25Z",
    "title_canon_sha256": "00a68d1e2cc5a2b2f705457cca0899c9ea0ad69bd2506a1cc714f49f99d42026"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.08504",
    "kind": "arxiv",
    "version": 2
  }
}