Pith Number

pith:JAAW3URS

pith:2012:JAAW3URS4YNXZ5STCF6RSBD27V

not attested not anchored not stored refs pending

Nonlinear spectral calculus and super-expanders

Assaf Naor, Manor Mendel

arxiv:1207.4705 v3 · 2012-07-19 · math.MG · math.CO · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JAAW3URS4YNXZ5STCF6RSBD27V}

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	2026-05-18T02:41:43.032728Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

48016dd232e61b7cf653117d19047afd41e30b4093f0a1af6aa665680d4b715c

Aliases

arxiv: 1207.4705 · arxiv_version: 1207.4705v3 · doi: 10.48550/arxiv.1207.4705 · pith_short_12: JAAW3URS4YNX · pith_short_16: JAAW3URS4YNXZ5ST · pith_short_8: JAAW3URS

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/JAAW3URS4YNXZ5STCF6RSBD27V \
  | 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: 48016dd232e61b7cf653117d19047afd41e30b4093f0a1af6aa665680d4b715c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d0f7f109fa7d65cd035ebb3b2efc00ce9f5114e61622c4f3ecdcc189f7410c5",
    "cross_cats_sorted": [
      "math.CO",
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-07-19T15:24:05Z",
    "title_canon_sha256": "d8fca0a315cb0b806f2aefa13bfad3c55eaee284eac16403b5d897aa53df99c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4705",
    "kind": "arxiv",
    "version": 3
  }
}