Pith Number

pith:VPK45LCB

pith:2015:VPK45LCBSN5WLXNWUNU6GIBTHZ

not attested not anchored not stored refs pending

Controlled Rough Paths on Manifolds I

Bruce K. Driver, Jeremy S. Semko

arxiv:1504.03308 v2 · 2015-04-13 · math.CA · math.DS · 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{VPK45LCBSN5WLXNWUNU6GIBTHZ}

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	2026-05-18T01:41:46.023938Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abd5ceac41937b65ddb6a369e320333e60aedbd6f2b73ac0643a5b89ed077783

Aliases

arxiv: 1504.03308 · arxiv_version: 1504.03308v2 · doi: 10.48550/arxiv.1504.03308 · pith_short_12: VPK45LCBSN5W · pith_short_16: VPK45LCBSN5WLXNW · pith_short_8: VPK45LCB

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/VPK45LCBSN5WLXNWUNU6GIBTHZ \
  | 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: abd5ceac41937b65ddb6a369e320333e60aedbd6f2b73ac0643a5b89ed077783

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbe02cfa1b14510173754d78c04fba9819eaf2ae8d7a5c182d8480ee147a792b",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2015-04-13T19:30:16Z",
    "title_canon_sha256": "fb95b38353894e58abfa193d62fd6d0ed1348f45991b6ed8136ec3ccd5e31b37"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1504.03308",
    "kind": "arxiv",
    "version": 2
  }
}