Pith Number

pith:64QHVEGM

pith:2016:64QHVEGMFEICKSHHZ2TE2NC4HS

not attested not anchored not stored refs pending

Spectral gap characterization of full type III factors

Amine Marrakchi

arxiv:1605.09613 v5 · 2016-05-31 · math.OA · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{64QHVEGMFEICKSHHZ2TE2NC4HS}

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	2026-05-18T00:58:55.164258Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7207a90cc29102548e7cea64d345c3c851c5c98a2f3f695b6a00659000af5fe

Aliases

arxiv: 1605.09613 · arxiv_version: 1605.09613v5 · doi: 10.48550/arxiv.1605.09613 · pith_short_12: 64QHVEGMFEIC · pith_short_16: 64QHVEGMFEICKSHH · pith_short_8: 64QHVEGM

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/64QHVEGMFEICKSHHZ2TE2NC4HS \
  | 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: f7207a90cc29102548e7cea64d345c3c851c5c98a2f3f695b6a00659000af5fe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ee29e8e483ae2b48d82424ea0a5dd7ff2ab86013649f56fab60346c55d83ea0",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2016-05-31T13:10:40Z",
    "title_canon_sha256": "1298724c8fb7eccdd4d41fc9f21c28f6862d2e1bf69c2539db36899abe7708f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.09613",
    "kind": "arxiv",
    "version": 5
  }
}