Pith Number

pith:R4UXRF7X

pith:2015:R4UXRF7XB4IJJQ5OBJTJCJJHDP

not attested not anchored not stored refs pending

On the Spectral Gap of a Quantum Graph

Delio Mugnolo, Gabriela Malenova, James B. Kennedy, Pavel Kurasov

arxiv:1504.01962 v2 · 2015-04-08 · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R4UXRF7XB4IJJQ5OBJTJCJJHDP}

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	2026-05-18T01:08:13.409961Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f297897f70f1094c3ae0a669125271be817d561709c399f6f16b66299996413

Aliases

arxiv: 1504.01962 · arxiv_version: 1504.01962v2 · doi: 10.48550/arxiv.1504.01962 · pith_short_12: R4UXRF7XB4IJ · pith_short_16: R4UXRF7XB4IJJQ5O · pith_short_8: R4UXRF7X

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/R4UXRF7XB4IJJQ5OBJTJCJJHDP \
  | 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: 8f297897f70f1094c3ae0a669125271be817d561709c399f6f16b66299996413

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4aa94a405f3131a94fe8caa53910fdce03ff8662ec0435252b1349fe488c3690",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-04-08T13:45:10Z",
    "title_canon_sha256": "dba166ad41f5f40757e3b534301f320ba208ad1bd76c137676d16e5c1938d3bf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.01962",
    "kind": "arxiv",
    "version": 2
  }
}