Pith Number

pith:GTX4Y7J5

pith:2018:GTX4Y7J5DFW3RLNQ4J2ENKXSRR

not attested not anchored not stored refs pending

Extremal Spectral Gaps for Periodic Schr\"odinger Operators

Braxton Osting, Chiu-Yen Kao

arxiv:1805.04210 v1 · 2018-05-11 · math.OC · 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{GTX4Y7J5DFW3RLNQ4J2ENKXSRR}

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	2026-05-18T00:16:13.242597Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34efcc7d3d196db8adb0e27446aaf28c6ba74080e5b6d83f93105947e76801b4

Aliases

arxiv: 1805.04210 · arxiv_version: 1805.04210v1 · doi: 10.48550/arxiv.1805.04210 · pith_short_12: GTX4Y7J5DFW3 · pith_short_16: GTX4Y7J5DFW3RLNQ · pith_short_8: GTX4Y7J5

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/GTX4Y7J5DFW3RLNQ4J2ENKXSRR \
  | 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: 34efcc7d3d196db8adb0e27446aaf28c6ba74080e5b6d83f93105947e76801b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c85d411fe276fa5b26c1d3693d362b8812d968df7de0aeae851c929af985f323",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2018-05-11T00:00:01Z",
    "title_canon_sha256": "fb2d72ff3b244b242b914b2e5f5deae44953c95eb70b36f52eeca96bc35cb9c0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.04210",
    "kind": "arxiv",
    "version": 1
  }
}