Pith Number

pith:DIVCVE4I

pith:2024:DIVCVE4IHCL6Z7Z6YMSNF7MEEQ

not attested not anchored not stored refs pending

Spectral properties of Sturm-Liouville operators on infinite metric graphs

Jia Zhao, Jun Yan, Yihan Liu

arxiv:2401.05649 v1 · 2024-01-11 · 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{DIVCVE4IHCL6Z7Z6YMSNF7MEEQ}

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	2026-07-05T07:32:32.989448Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a2a2a93883897ecff3ec324d2fd84242ff9304fc53d35aaad22c542aa737106

Aliases

arxiv: 2401.05649 · arxiv_version: 2401.05649v1 · doi: 10.48550/arxiv.2401.05649 · pith_short_12: DIVCVE4IHCL6 · pith_short_16: DIVCVE4IHCL6Z7Z6 · pith_short_8: DIVCVE4I

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/DIVCVE4IHCL6Z7Z6YMSNF7MEEQ \
  | 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: 1a2a2a93883897ecff3ec324d2fd84242ff9304fc53d35aaad22c542aa737106

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47bc409ad242fee071760f97055014d96abd6b5110cd0006235835ca9c3fa845",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2024-01-11T04:01:48Z",
    "title_canon_sha256": "f44328e32061a67d884830bc24a45659245cb32528e2167448336c169ae87a63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2401.05649",
    "kind": "arxiv",
    "version": 1
  }
}