Pith Number

pith:LPLDX3FI

pith:2009:LPLDX3FI53BENI4U7PWY445FZE

not attested not anchored not stored refs pending

High-frequency averaging in semi-classical Hartree-type equations

Alexander Mielke, Christof Sparber, Johannes Giannoulis

arxiv:0909.5640 v2 · 2009-09-30 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPLDX3FI53BENI4U7PWY445FZE}

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	2026-05-18T00:26:02.766613Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd63beca8eec246a394fbed8e73a5c93426aecfc08dfdbc8ac3203023f79cd6

Aliases

arxiv: 0909.5640 · arxiv_version: 0909.5640v2 · doi: 10.48550/arxiv.0909.5640 · pith_short_12: LPLDX3FI53BE · pith_short_16: LPLDX3FI53BENI4U · pith_short_8: LPLDX3FI

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/LPLDX3FI53BENI4U7PWY445FZE \
  | 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: 5bd63beca8eec246a394fbed8e73a5c93426aecfc08dfdbc8ac3203023f79cd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "262b126f6bd2ce401583462e28fcb30f239220bfee83f02f429492fc5e6ee921",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2009-09-30T15:47:20Z",
    "title_canon_sha256": "4ac4fe7bf7947fdbe995ff8f6ecebff8abc0efecf63ef35ae75ade6749098734"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.5640",
    "kind": "arxiv",
    "version": 2
  }
}