Pith Number

pith:CTEKYSD2

pith:2011:CTEKYSD2NKIJT6BAT7UIBZNPEK

not attested not anchored not stored refs pending

Lifshitz formula by spectral summation method

I. G. Pirozhenko, V. V. Nesterenko

arxiv:1112.2599 v3 · 2011-12-12 · quant-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CTEKYSD2NKIJT6BAT7UIBZNPEK}

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	2026-05-18T01:59:11.694487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14c8ac487a6a9099f8209fe880e5af22a7da5f05fcdb79368956d5fb46599efa

Aliases

arxiv: 1112.2599 · arxiv_version: 1112.2599v3 · doi: 10.48550/arxiv.1112.2599 · pith_short_12: CTEKYSD2NKIJ · pith_short_16: CTEKYSD2NKIJT6BA · pith_short_8: CTEKYSD2

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/CTEKYSD2NKIJT6BAT7UIBZNPEK \
  | 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: 14c8ac487a6a9099f8209fe880e5af22a7da5f05fcdb79368956d5fb46599efa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "10abdde7d9dde7743e04b8e420ff2924b0567f521abc59f098aeccddc8d8b42f",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2011-12-12T16:06:42Z",
    "title_canon_sha256": "cd1229e972542508dae9812477c399f5147268e322d1f2deb2bf3351ad9dc850"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2599",
    "kind": "arxiv",
    "version": 3
  }
}