Pith Number

pith:NUUMMH5U

pith:2013:NUUMMH5UMUXKFLOUIISPPEHKSY

not attested not anchored not stored refs pending

Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE

Adam Andersson, Raphael Kruse, Stig Larsson

arxiv:1312.5893 v3 · 2013-12-20 · math.PR · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NUUMMH5UMUXKFLOUIISPPEHKSY}

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	2026-05-18T01:20:17.874282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d28c61fb4652ea2add44224f790ea96200e9b1851ae483222a31643353092b9

Aliases

arxiv: 1312.5893 · arxiv_version: 1312.5893v3 · doi: 10.48550/arxiv.1312.5893 · pith_short_12: NUUMMH5UMUXK · pith_short_16: NUUMMH5UMUXKFLOU · pith_short_8: NUUMMH5U

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/NUUMMH5UMUXKFLOUIISPPEHKSY \
  | 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: 6d28c61fb4652ea2add44224f790ea96200e9b1851ae483222a31643353092b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "13139b9fa4c72fc6d00ec89b7f1e894125504080d65ab487f3899605506cd138",
    "cross_cats_sorted": [
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-12-20T11:19:09Z",
    "title_canon_sha256": "d3f70b2905988e582438646e817cb86276a69bfb3e7f0752f560be1d2f0dca61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.5893",
    "kind": "arxiv",
    "version": 3
  }
}