Pith Number

pith:PTU6SB5P

pith:2011:PTU6SB5PWP5G3ASCPGWKOSK2L3

not attested not anchored not stored refs pending

Algebraic spectral gaps

Amaury Mouchet (LMPT)

arxiv:1111.0656 v1 · 2011-11-02 · math-ph · math.MP · math.SP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PTU6SB5PWP5G3ASCPGWKOSK2L3}

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	2026-05-18T04:09:36.105196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ce9e907afb3fa6d824279aca7495a5ede35c2cf6834cd2ea9d4ff1883e5cd1a

Aliases

arxiv: 1111.0656 · arxiv_version: 1111.0656v1 · doi: 10.48550/arxiv.1111.0656 · pith_short_12: PTU6SB5PWP5G · pith_short_16: PTU6SB5PWP5G3ASC · pith_short_8: PTU6SB5P

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/PTU6SB5PWP5G3ASCPGWKOSK2L3 \
  | 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: 7ce9e907afb3fa6d824279aca7495a5ede35c2cf6834cd2ea9d4ff1883e5cd1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "67d221f0b0e0d1dfd23bf2722006088eeba6a61ebb08de269a15be4b1f357eb2",
    "cross_cats_sorted": [
      "math.MP",
      "math.SP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-11-02T20:52:18Z",
    "title_canon_sha256": "6ac1277d13e766251e0b5594545e9066fea39c8563d74293ad29a072472c1928"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.0656",
    "kind": "arxiv",
    "version": 1
  }
}