Pith Number

pith:7YL23SAV

pith:2011:7YL23SAVCPSYGD2JT5TMYKA7FU

not attested not anchored not stored refs pending

Spectral gap lower bound for the one-dimensional fractional Schr\"odinger operator in the interval

Kamil Kaleta

arxiv:1104.3502 v2 · 2011-04-18 · math.PR · 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{7YL23SAVCPSYGD2JT5TMYKA7FU}

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	2026-05-18T02:57:24.427410Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe17adc81513e5830f499f66cc281f2d00341e3d680c062450639f475bfca6e5

Aliases

arxiv: 1104.3502 · arxiv_version: 1104.3502v2 · doi: 10.48550/arxiv.1104.3502 · pith_short_12: 7YL23SAVCPSY · pith_short_16: 7YL23SAVCPSYGD2J · pith_short_8: 7YL23SAV

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/7YL23SAVCPSYGD2JT5TMYKA7FU \
  | 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: fe17adc81513e5830f499f66cc281f2d00341e3d680c062450639f475bfca6e5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5723095a5ddf06c5e347571e77562f704ae013c4452849c5ad09e3bdca3b081d",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-04-18T14:54:40Z",
    "title_canon_sha256": "23119308243b4a5196a78baa8f8bf518025174bf27a36b4741ab54def15bcf03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3502",
    "kind": "arxiv",
    "version": 2
  }
}