Pith Number

pith:HRFYWMRS

pith:2012:HRFYWMRSYT6AMUZRLPVTPCI7XM

not attested not anchored not stored refs pending

Characterization of potential smoothness and Riesz basis property of the Hill-Scr\"odinger operator in terms of periodic, antiperiodic and Neumann spectra

Ahmet Batal

arxiv:1207.0948 v1 · 2012-07-04 · math.SP · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HRFYWMRSYT6AMUZRLPVTPCI7XM}

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	2026-05-18T03:51:47.885360Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3c4b8b3232c4fc0653315beb37891fbb0e2dfe67cbb744d75adf2f937262bf2a

Aliases

arxiv: 1207.0948 · arxiv_version: 1207.0948v1 · doi: 10.48550/arxiv.1207.0948 · pith_short_12: HRFYWMRSYT6A · pith_short_16: HRFYWMRSYT6AMUZR · pith_short_8: HRFYWMRS

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/HRFYWMRSYT6AMUZRLPVTPCI7XM \
  | 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: 3c4b8b3232c4fc0653315beb37891fbb0e2dfe67cbb744d75adf2f937262bf2a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "631835795ff3f78c7dd23409034ccb628bed94dfa4ffd75fe0903e839658c736",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2012-07-04T11:52:25Z",
    "title_canon_sha256": "ab3c4ced8c9d7fed7c74a8bbef78aa492a861cd98b586f2750c3290e9912a607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0948",
    "kind": "arxiv",
    "version": 1
  }
}