Pith Number

pith:LMLSDIPR

pith:2010:LMLSDIPR4PYYGJXDAV4YKDWB6O

not attested not anchored not stored refs pending

A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection

Konstantinos Spiliopoulos

arxiv:1004.3043 v1 · 2010-04-18 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LMLSDIPR4PYYGJXDAV4YKDWB6O}

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	2026-05-18T04:34:37.144304Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5b1721a1f1e3f18326e30579850ec1f3ac9e1980d570b40224b387e42e99d7e8

Aliases

arxiv: 1004.3043 · arxiv_version: 1004.3043v1 · doi: 10.48550/arxiv.1004.3043 · pith_short_12: LMLSDIPR4PYY · pith_short_16: LMLSDIPR4PYYGJXD · pith_short_8: LMLSDIPR

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/LMLSDIPR4PYYGJXDAV4YKDWB6O \
  | 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: 5b1721a1f1e3f18326e30579850ec1f3ac9e1980d570b40224b387e42e99d7e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "000e4064b8b230c7af1e07f0ce24a4f98870d283afc29b9cbba88b66a9f28494",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-04-18T17:43:39Z",
    "title_canon_sha256": "feb0177dbd7d21434148b05da27efd58213bf3c2979ffce5434858f09829fbd6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.3043",
    "kind": "arxiv",
    "version": 1
  }
}