Pith Number

pith:S64VIJLE

pith:2026:S64VIJLE6AEWCNUNFO62QU4657

not attested not anchored not stored refs pending

Stochastic Approximation in Banach Spaces Without Geometric Constraints

B V Rao, Rajeeva Laxman Karandikar

arxiv:2607.10356 v1 · 2026-07-11 · 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{S64VIJLE6AEWCNUNFO62QU4657}

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	2026-07-14T01:21:11.567908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97b9542564f00961368d2bbda8539eefe079b4eaedbc6c81ee203f39ee84a5c5

Aliases

arxiv: 2607.10356 · arxiv_version: 2607.10356v1 · doi: 10.48550/arxiv.2607.10356 · pith_short_12: S64VIJLE6AEW · pith_short_16: S64VIJLE6AEWCNUN · pith_short_8: S64VIJLE

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/S64VIJLE6AEWCNUNFO62QU4657 \
  | 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: 97b9542564f00961368d2bbda8539eefe079b4eaedbc6c81ee203f39ee84a5c5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ba99adead53d6f4f6eb0f30a62e44839c8988e6abad44ef4a8072fba3bbc2c05",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-11T15:29:31Z",
    "title_canon_sha256": "6ec1c203c1154ff8a30965e472661cb74783798f67f6fd852ce4506b44db3813"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10356",
    "kind": "arxiv",
    "version": 1
  }
}