Pith Number

pith:DEKZDGKY

pith:2011:DEKZDGKY6AYO3WMZMBXJKK4WZ5

not attested not anchored not stored refs pending

2-microlocal analysis of martingales and stochastic integrals

Erick Herbin, Paul Balan\c{c}a

arxiv:1107.6016 v2 · 2011-07-29 · 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{DEKZDGKY6AYO3WMZMBXJKK4WZ5}

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	2026-05-18T03:14:50.415509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d

Aliases

arxiv: 1107.6016 · arxiv_version: 1107.6016v2 · doi: 10.48550/arxiv.1107.6016 · pith_short_12: DEKZDGKY6AYO · pith_short_16: DEKZDGKY6AYO3WMZ · pith_short_8: DEKZDGKY

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/DEKZDGKY6AYO3WMZMBXJKK4WZ5 \
  | 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: 1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b13a8bb423e5dfc35d419bcd2b60c06d60897d4778ffb9ea03e5a23d3266b278",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-07-29T16:44:16Z",
    "title_canon_sha256": "91107b2a70b85909ff4f2240c8ad9a20244feaadb494c55e5bcd9cd3c9e5db45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.6016",
    "kind": "arxiv",
    "version": 2
  }
}