Pith Number

pith:VLBLE6CB

pith:2015:VLBLE6CBFLF3JSDX7TWRMGM45C

not attested not anchored not stored refs pending

Symmetries of Stochastic Differential Equations: a geometric approach

Francesco C. De Vecchi, Paola Morando, Stefania Ugolini

arxiv:1512.05215 v1 · 2015-12-16 · math.PR · 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{VLBLE6CBFLF3JSDX7TWRMGM45C}

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	2026-05-18T01:10:14.828890Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aac2b278412acbb4c877fced16199ce8a633ae5f30357195613b12b5d647fa1a

Aliases

arxiv: 1512.05215 · arxiv_version: 1512.05215v1 · doi: 10.48550/arxiv.1512.05215 · pith_short_12: VLBLE6CBFLF3 · pith_short_16: VLBLE6CBFLF3JSDX · pith_short_8: VLBLE6CB

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/VLBLE6CBFLF3JSDX7TWRMGM45C \
  | 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: aac2b278412acbb4c877fced16199ce8a633ae5f30357195613b12b5d647fa1a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4ee59da63bb276dc3b35a6e53a608d189886cbe22c4732a3b77b8a0e0eadc23",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-16T15:41:33Z",
    "title_canon_sha256": "1aa107ced6e0383eeee88657d50d93ec4dea144d437e73bf66b1fd273cba7255"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.05215",
    "kind": "arxiv",
    "version": 1
  }
}