Pith Number

pith:PYVMVXS6

pith:2013:PYVMVXS6DVKAF2YPXSUBCRHJHH

not attested not anchored not stored refs pending

On band spectrum of Schroedinger operator in periodic system of domains coupled by small windows

Denis Borisov

arxiv:1312.7534 v1 · 2013-12-29 · math.SP · math-ph · math.AP · 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{PYVMVXS6DVKAF2YPXSUBCRHJHH}

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	2026-05-18T03:03:43.129554Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7e2acade5e1d5402eb0fbca81144e939d2345c4cb172cd8b8103ed5dd53c9436

Aliases

arxiv: 1312.7534 · arxiv_version: 1312.7534v1 · doi: 10.48550/arxiv.1312.7534 · pith_short_12: PYVMVXS6DVKA · pith_short_16: PYVMVXS6DVKAF2YP · pith_short_8: PYVMVXS6

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/PYVMVXS6DVKAF2YPXSUBCRHJHH \
  | 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: 7e2acade5e1d5402eb0fbca81144e939d2345c4cb172cd8b8103ed5dd53c9436

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d96a74cadcfc89df679721492fb6054e3d009719f8d694cf9ea35592f1d1a366",
    "cross_cats_sorted": [
      "math-ph",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2013-12-29T13:18:35Z",
    "title_canon_sha256": "f343f1c9e7a8c2d7baed8e255a6b0c4f8af9f019989498cda361373401de2a10"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.7534",
    "kind": "arxiv",
    "version": 1
  }
}