Pith Number

pith:DPKDUGAF

pith:2012:DPKDUGAFYTZA25YMTK3Y3KLYCG

not attested not anchored not stored refs pending

Homogenization at different linear scales, bounded martingales and the Two-Scale Shuffle limit

INRIA Bordeaux - Sud-Ouest), K\'evin Santugini-Repiquet (IMB

arxiv:1209.6145 v1 · 2012-09-27 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DPKDUGAFYTZA25YMTK3Y3KLYCG}

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	2026-05-18T03:03:21.288343Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1bd43a1805c4f20d770c9ab78da978118400f1df418c999171ade23692daa09b

Aliases

arxiv: 1209.6145 · arxiv_version: 1209.6145v1 · doi: 10.48550/arxiv.1209.6145 · pith_short_12: DPKDUGAFYTZA · pith_short_16: DPKDUGAFYTZA25YM · pith_short_8: DPKDUGAF

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/DPKDUGAFYTZA25YMTK3Y3KLYCG \
  | 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: 1bd43a1805c4f20d770c9ab78da978118400f1df418c999171ade23692daa09b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20c6aece7c231e87d69e11540d2019a68d96c9209c7592e58d4d589f5512e880",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-27T07:24:42Z",
    "title_canon_sha256": "cd9a324beadf55a96c31573c46ff6e87bcf44ffac6adb7a1dab9778e006c0d38"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.6145",
    "kind": "arxiv",
    "version": 1
  }
}