Pith Number

pith:AENT6L6Y

pith:2016:AENT6L6YVLZ4RSXFWMJ2SSAFXP

not attested not anchored not stored refs pending

Piecewise constant local martingales with bounded numbers of jumps

Johannes Ruf

arxiv:1612.08038 v1 · 2016-12-23 · 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{AENT6L6YVLZ4RSXFWMJ2SSAFXP}

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	2026-05-18T00:54:05.059657Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

011b3f2fd8aaf3c8cae5b313a94805bbe07d76c3f6c08adc9bc00404c67b3731

Aliases

arxiv: 1612.08038 · arxiv_version: 1612.08038v1 · doi: 10.48550/arxiv.1612.08038 · pith_short_12: AENT6L6YVLZ4 · pith_short_16: AENT6L6YVLZ4RSXF · pith_short_8: AENT6L6Y

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/AENT6L6YVLZ4RSXFWMJ2SSAFXP \
  | 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: 011b3f2fd8aaf3c8cae5b313a94805bbe07d76c3f6c08adc9bc00404c67b3731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4f3a619194ef6acd1054fbdce1450c2a702cfc2c14cf5ae99302eea4f7fdc41",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-12-23T17:03:05Z",
    "title_canon_sha256": "45d9730a6ac854e9949b3c59763295b89f2da06f69c93edf84a80800841db33e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08038",
    "kind": "arxiv",
    "version": 1
  }
}