Pith Number

pith:2Z23RHCE

pith:2026:2Z23RHCERYUWZEJZ36EZ5PRFHU

not attested not anchored not stored refs pending

Higher-order variation and pathwise Ito calculus on manifolds

Rama Cont

arxiv:2608.12225 v1 · 2026-08-12 · math.PR · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2Z23RHCERYUWZEJZ36EZ5PRFHU}

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	2026-08-13T01:30:33.270093Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d675b89c448e296c9139df899ebe253d0f2940d4b695cd487121820ed6d08f52

Aliases

arxiv: 2608.12225 · arxiv_version: 2608.12225v1 · doi: 10.48550/arxiv.2608.12225 · pith_short_12: 2Z23RHCERYUW · pith_short_16: 2Z23RHCERYUWZEJZ · pith_short_8: 2Z23RHCE

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/2Z23RHCERYUWZEJZ36EZ5PRFHU \
  | 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: d675b89c448e296c9139df899ebe253d0f2940d4b695cd487121820ed6d08f52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b37c6295ff23503f84ff10e5eb381975bd16d69fee2f7b3371fb689a0a07171d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-08-12T16:22:45Z",
    "title_canon_sha256": "fba665e43c09aaf73bd44777f685f029e720f460088ca42907755887914afc6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.12225",
    "kind": "arxiv",
    "version": 1
  }
}