Pith Number

pith:GYM4JEZS

pith:2015:GYM4JEZSBQ7Z64W5NLEUF7SA2Z

not attested not anchored not stored refs pending

Muckenhoupt's $(A_p)$ condition and the existence of the optimal martingale measure

Dmitry Kramkov, Kim Weston

arxiv:1507.05865 v1 · 2015-07-21 · q-fin.MF

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GYM4JEZSBQ7Z64W5NLEUF7SA2Z}

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	2026-05-18T00:51:58.301897Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3619c493320c3f9f72dd6ac942fe40d67c75ac4e2ae442b05b20eefcfae97242

Aliases

arxiv: 1507.05865 · arxiv_version: 1507.05865v1 · doi: 10.48550/arxiv.1507.05865 · pith_short_12: GYM4JEZSBQ7Z · pith_short_16: GYM4JEZSBQ7Z64W5 · pith_short_8: GYM4JEZS

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/GYM4JEZSBQ7Z64W5NLEUF7SA2Z \
  | 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: 3619c493320c3f9f72dd6ac942fe40d67c75ac4e2ae442b05b20eefcfae97242

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad1a729095e41cebc6a0545cf7377351e5527838a44308b1d9d99a63f6b853a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-fin.MF",
    "submitted_at": "2015-07-21T15:08:29Z",
    "title_canon_sha256": "c60235fa571a7c658e6fea619a92b790a846db2e345d836446c19b424f5e753b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.05865",
    "kind": "arxiv",
    "version": 1
  }
}