Pith Number

pith:TVYLKW6E

pith:2015:TVYLKW6E7FDTVVMCIT43DWG4MA

not attested not anchored not stored refs pending

Gaps in the spectrum of a periodic quantum graph with periodically distributed $\delta'$-type interactions

Andrii Khrabustovskyi, Diana Barseghyan

arxiv:1502.04664 v1 · 2015-02-16 · math.SP · math-ph · 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{TVYLKW6E7FDTVVMCIT43DWG4MA}

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	2026-05-18T02:26:59.385523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d70b55bc4f9473ad58244f9b1d8dc601b34383f67332c0592a433c1eff44ed8

Aliases

arxiv: 1502.04664 · arxiv_version: 1502.04664v1 · doi: 10.48550/arxiv.1502.04664 · pith_short_12: TVYLKW6E7FDT · pith_short_16: TVYLKW6E7FDTVVMC · pith_short_8: TVYLKW6E

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/TVYLKW6E7FDTVVMCIT43DWG4MA \
  | 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: 9d70b55bc4f9473ad58244f9b1d8dc601b34383f67332c0592a433c1eff44ed8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3587504addf24ec8742bebce0cca9adf70ca01da1421186ee12bff46330acae",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2015-02-16T19:00:34Z",
    "title_canon_sha256": "f2b70d2e67b9689278ad8d50d0541d6f277ff2083b7948df87b5ded0aab28444"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1502.04664",
    "kind": "arxiv",
    "version": 1
  }
}