Pith Number

pith:GJMAVI5K

pith:2015:GJMAVI5K6SUJSZPJG7KGOOQC42

not attested not anchored not stored refs pending

Shell Polynomials and Dual Birth-Death Processes

Erik A. van Doorn

arxiv:1512.07104 v2 · 2015-12-22 · 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{GJMAVI5K6SUJSZPJG7KGOOQC42}

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	2026-05-18T01:14:35.675853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32580aa3aaf4a89965e937d4673a02e68b049ad30262e15ec8f9fa77a5095347

Aliases

arxiv: 1512.07104 · arxiv_version: 1512.07104v2 · doi: 10.48550/arxiv.1512.07104 · pith_short_12: GJMAVI5K6SUJ · pith_short_16: GJMAVI5K6SUJSZPJ · pith_short_8: GJMAVI5K

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/GJMAVI5K6SUJSZPJG7KGOOQC42 \
  | 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: 32580aa3aaf4a89965e937d4673a02e68b049ad30262e15ec8f9fa77a5095347

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cda1d87753d3d11059190c4bd25e4439f2b317470599189568b4ca4a40d5ea18",
    "cross_cats_sorted": [
      "math.CA"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-12-22T14:33:19Z",
    "title_canon_sha256": "125182bc4220aec4b724f0734230bff20b95fa8ef831547acc42a272d248ec00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.07104",
    "kind": "arxiv",
    "version": 2
  }
}