Pith Number

pith:O7C2TI5U

pith:2016:O7C2TI5ULWHHIUNLP6NJQY2PEY

not attested not anchored not stored refs pending

Spectral and scattering theory for Gauss-Bonnet operators on perturbed topological crystals

Daniel Parra

arxiv:1609.02260 v1 · 2016-09-08 · math.SP · 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{O7C2TI5ULWHHIUNLP6NJQY2PEY}

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	2026-05-17T23:56:34.601693Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77c5a9a3b45d8e7451ab7f9a98634f26167a83646e9832a54edef9e5659e79df

Aliases

arxiv: 1609.02260 · arxiv_version: 1609.02260v1 · doi: 10.48550/arxiv.1609.02260 · pith_short_12: O7C2TI5ULWHH · pith_short_16: O7C2TI5ULWHHIUNL · pith_short_8: O7C2TI5U

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/O7C2TI5ULWHHIUNLP6NJQY2PEY \
  | 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: 77c5a9a3b45d8e7451ab7f9a98634f26167a83646e9832a54edef9e5659e79df

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86d228299a5c1c1cf23c329387fd31774745368797e61e9d1d3d4eaa0693cd41",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2016-09-08T04:07:23Z",
    "title_canon_sha256": "f3c31935500221c18cf46d8edf01038846b4e410b19c54f172adc2a120cd1c87"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.02260",
    "kind": "arxiv",
    "version": 1
  }
}