Pith Number

pith:VB4YJ725

pith:2013:VB4YJ72522EUM7KTCGFSENMX4P

not attested not anchored not stored refs pending

Linear hyperbolic PDEs with non-commutative time

Gandalf Lechner, Rainer Verch

arxiv:1307.1780 v2 · 2013-07-06 · math-ph · hep-th · 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{VB4YJ72522EUM7KTCGFSENMX4P}

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

The Cauchy Problem for Symmetric Hyperbolic Systems with Nonlocal Potentials

Receipt and verification

First computed	2026-07-05T03:13:59.414287Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819

Aliases

arxiv: 1307.1780 · arxiv_version: 1307.1780v2 · doi: 10.48550/arxiv.1307.1780 · pith_short_12: VB4YJ72522EU · pith_short_16: VB4YJ72522EUM7KT · pith_short_8: VB4YJ725

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/VB4YJ72522EUM7KTCGFSENMX4P \
  | 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: a87984ff5dd689467d53118b223597e3dca740e649ff7a9c88e935be8df50819

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42e3a87d5a71873f8eaacd187dd03231c625ae859703d1f82ed5a7b4857785b6",
    "cross_cats_sorted": [
      "hep-th",
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-07-06T13:26:09Z",
    "title_canon_sha256": "ab4ed1b75209f226a3314eb1bff0b614ec1656829bc80ea94a0ba697003eb986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1307.1780",
    "kind": "arxiv",
    "version": 2
  }
}