Pith Number

pith:OSLK7QJ2

pith:2017:OSLK7QJ2A5J2DKIG5HPA7HYYAQ

not attested not anchored not stored refs pending

Criticality theory for Schr\"odinger operators on graphs

Felix Pogorzelski, Matthias Keller, Yehuda Pinchover

arxiv:1708.09664 v1 · 2017-08-31 · math.SP · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OSLK7QJ2A5J2DKIG5HPA7HYYAQ}

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	2026-05-18T00:36:15.809485Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7496afc13a0753a1a906e9de0f9f18041354678784f59a01875b677b165787ed

Aliases

arxiv: 1708.09664 · arxiv_version: 1708.09664v1 · doi: 10.48550/arxiv.1708.09664 · pith_short_12: OSLK7QJ2A5J2 · pith_short_16: OSLK7QJ2A5J2DKIG · pith_short_8: OSLK7QJ2

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/OSLK7QJ2A5J2DKIG5HPA7HYYAQ \
  | 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: 7496afc13a0753a1a906e9de0f9f18041354678784f59a01875b677b165787ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f96b892c1e36ec818b8eca24f030c2a54250a8dc4afc392d151fcdb0eedb735d",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2017-08-31T11:12:47Z",
    "title_canon_sha256": "0c680a7defe2328f07ee88eaa01a410612beeb3135ef370557585f4a01818030"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1708.09664",
    "kind": "arxiv",
    "version": 1
  }
}