Pith Number

pith:PQJEXPI5

pith:2019:PQJEXPI56HA3CWXKKHMDNPOAOB

not attested not anchored not stored refs pending

Analytic expressions for Debye functions and the heat capacity of a solid

Alfredo Vega, Igor Kondrashuk, Ivan Gonzalez, Victor H. Moll

arxiv:1908.08667 v1 · 2019-08-23 · 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{PQJEXPI56HA3CWXKKHMDNPOAOB}

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.

Cited by

1 paper in Pith

Inverse Laplace and Mellin integral transforms modified for use in quantum communications

Receipt and verification

First computed	2026-07-05T04:32:46.424667Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7c124bbd1df1c1b15aea51d836bdc0705fabd1488db7f4d140b79d823df3c52b

Aliases

arxiv: 1908.08667 · arxiv_version: 1908.08667v1 · doi: 10.48550/arxiv.1908.08667 · pith_short_12: PQJEXPI56HA3 · pith_short_16: PQJEXPI56HA3CWXK · pith_short_8: PQJEXPI5

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/PQJEXPI56HA3CWXKKHMDNPOAOB \
  | 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: 7c124bbd1df1c1b15aea51d836bdc0705fabd1488db7f4d140b79d823df3c52b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41bdaf7bed06a341c4afee5962f9678b181b92204cb96fbffe980bc433dc0d18",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-08-23T05:12:30Z",
    "title_canon_sha256": "1faec7fad4afe1f670362bc20e2f0c5c59c1435afe48770bdb0b1320fa7a9b0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08667",
    "kind": "arxiv",
    "version": 1
  }
}