Pith Number

pith:HJ5YG4WX

pith:2016:HJ5YG4WX6AAPUL762KELA5ARWM

not attested not anchored not stored refs pending

Strict Local Martingales via Filtration Enlargement

Aditi Dandapani, Philip Protter

arxiv:1608.06361 v1 · 2016-08-23 · 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{HJ5YG4WX6AAPUL762KELA5ARWM}

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	2026-05-18T01:08:14.240692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a7b8372d7f000fa2ffed288b07411b32b49cd8c0b04ed4c25d868df7d20ecaf

Aliases

arxiv: 1608.06361 · arxiv_version: 1608.06361v1 · doi: 10.48550/arxiv.1608.06361 · pith_short_12: HJ5YG4WX6AAP · pith_short_16: HJ5YG4WX6AAPUL76 · pith_short_8: HJ5YG4WX

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/HJ5YG4WX6AAPUL762KELA5ARWM \
  | 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: 3a7b8372d7f000fa2ffed288b07411b32b49cd8c0b04ed4c25d868df7d20ecaf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca1a62a419e128fb08a8927389c416e8a090bd4f1d4a91068610fd06d42a4ae3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-08-23T02:17:08Z",
    "title_canon_sha256": "43b8cabbbd79bd781627f4e58a61300456f7e1be9aa101e2b5940cbc2c7dcc03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.06361",
    "kind": "arxiv",
    "version": 1
  }
}