Pith Number

pith:MMGAM3ZR

pith:2013:MMGAM3ZRWK4XAP4PS7GXOC7FO7

not attested not anchored not stored refs pending

Asymptotic formulas for spectral gaps and deviations of Hill and 1D Dirac operators

Boris Mityagin, Plamen Djakov

arxiv:1309.1751 v1 · 2013-09-06 · 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{MMGAM3ZRWK4XAP4PS7GXOC7FO7}

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	2026-05-18T03:13:58.717590Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

630c066f31b2b9703f8f97cd770be577d1cd09d0bcf48ce6a1f2ba644b385cf8

Aliases

arxiv: 1309.1751 · arxiv_version: 1309.1751v1 · doi: 10.48550/arxiv.1309.1751 · pith_short_12: MMGAM3ZRWK4X · pith_short_16: MMGAM3ZRWK4XAP4P · pith_short_8: MMGAM3ZR

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/MMGAM3ZRWK4XAP4PS7GXOC7FO7 \
  | 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: 630c066f31b2b9703f8f97cd770be577d1cd09d0bcf48ce6a1f2ba644b385cf8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a7a0386bba91e61f932cf5480fe0f03b15512205254e0e573cac8c7d1d59de9e",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-09-06T19:41:43Z",
    "title_canon_sha256": "dd54478398b1936d56d172b58289557acf6d979b1f2422d6057b409e6b948cea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.1751",
    "kind": "arxiv",
    "version": 1
  }
}