Pith Number

pith:MPF3IP6F

pith:2026:MPF3IP6F2TZIGGTTFMCQTG3F7J

not attested not anchored not stored refs pending

Binomial probabilities at a fixed distance from the mode: size-biasing and the complete asymptotic expansion

Neven Elezovi\'c

arxiv:2607.19844 v1 · 2026-07-22 · math.PR · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MPF3IP6F2TZIGGTTFMCQTG3F7J}

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.

Cited by

1 paper in Pith

The mean absolute deviation of the classical discrete distributions: collapse identities, complete asymptotic expansions, and enveloping series

Receipt and verification

First computed	2026-07-23T01:24:03.269443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63cbb43fc5d4f2831a732b05099b65fa794815b59b55f02d58d3b55436490dae

Aliases

arxiv: 2607.19844 · arxiv_version: 2607.19844v1 · doi: 10.48550/arxiv.2607.19844 · pith_short_12: MPF3IP6F2TZI · pith_short_16: MPF3IP6F2TZIGGTT · pith_short_8: MPF3IP6F

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/MPF3IP6F2TZIGGTTFMCQTG3F7J \
  | 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: 63cbb43fc5d4f2831a732b05099b65fa794815b59b55f02d58d3b55436490dae

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4125495670b01e401c3ba46f7f52b39d51588edfe39b5c96f2250c44a4a98129",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-07-22T07:30:15Z",
    "title_canon_sha256": "feeee16a5e428b8fc6e689f9641e7a543a5783d58c3e9d858a3d89d1f1731369"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19844",
    "kind": "arxiv",
    "version": 1
  }
}