Pith Number

pith:GCEBHC2A

pith:2013:GCEBHC2AIAR377SE2F6OH574BH

not attested not anchored not stored refs pending

Exponential Time Decay Estimates for the Landau Equation on Torus

Kung-Chien Wu

arxiv:1301.0827 v1 · 2013-01-04 · 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{GCEBHC2AIAR377SE2F6OH574BH}

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	2026-05-18T03:37:07.619870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3088138b404023bffe44d17ce3f7fc09f395b2b174951a9300f3ce0fdf6f429e

Aliases

arxiv: 1301.0827 · arxiv_version: 1301.0827v1 · doi: 10.48550/arxiv.1301.0827 · pith_short_12: GCEBHC2AIAR3 · pith_short_16: GCEBHC2AIAR377SE · pith_short_8: GCEBHC2A

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/GCEBHC2AIAR377SE2F6OH574BH \
  | 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: 3088138b404023bffe44d17ce3f7fc09f395b2b174951a9300f3ce0fdf6f429e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b50a138f291ef697bb92d41dd74670f7c7f330caf28ae0ebeb4f67cd2ae0540",
    "cross_cats_sorted": [
      "math.AP",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-01-04T14:37:47Z",
    "title_canon_sha256": "59b59557cc0abb766665dffc61d9a66fd17854ed6cba35b523afc77faf627225"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1301.0827",
    "kind": "arxiv",
    "version": 1
  }
}