Pith Number

pith:5YP2SK4M

pith:2011:5YP2SK4M6U74EUMSYFJCDYYKVL

not attested not anchored not stored refs pending

Spectral estimates for the Schr\"odinger operators with sparse potentials on graphs

Grigori Rozenblum, Michael Solomyak

arxiv:1104.3455 v1 · 2011-04-18 · 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{5YP2SK4M6U74EUMSYFJCDYYKVL}

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	2026-05-18T04:24:05.038140Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee1fa92b8cf53fc25192c15221e30aaad8d18efb6ef0745cab1d4fedf75a7505

Aliases

arxiv: 1104.3455 · arxiv_version: 1104.3455v1 · doi: 10.48550/arxiv.1104.3455 · pith_short_12: 5YP2SK4M6U74 · pith_short_16: 5YP2SK4M6U74EUMS · pith_short_8: 5YP2SK4M

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/5YP2SK4M6U74EUMSYFJCDYYKVL \
  | 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: ee1fa92b8cf53fc25192c15221e30aaad8d18efb6ef0745cab1d4fedf75a7505

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7ec643207abbe0f3225beb991cbb743096346186ec7a0975ea234e1d6fcff848",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2011-04-18T12:30:10Z",
    "title_canon_sha256": "c202c6509705ec7972b0d6eeefa0be40ee17eaf1a1008392a7d7d88e770e0fc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3455",
    "kind": "arxiv",
    "version": 1
  }
}