Pith Number

pith:GEMZFZD6

pith:2025:GEMZFZD62ESF6LGRW2DM6JHLUR

not attested not anchored not stored refs pending

Long time behavior and Yaglom limit for real trait-structured Birth and Death Processes

CMAP), Jaime San (CMM), Pierre Collet (CPHT), Sylvie M\'el\'eard (MERGE

arxiv:2508.04089 v1 · 2025-08-06 · 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{GEMZFZD62ESF6LGRW2DM6JHLUR}

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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

Long-Time Behaviors of Branching-Diffusion Processes via Spectral Analysis

Receipt and verification

First computed	2026-07-05T11:49:20.455125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

311992e47ed1245f2cd1b686cf24eba463202e218af09d680b43e8565b280d5a

Aliases

arxiv: 2508.04089 · arxiv_version: 2508.04089v1 · doi: 10.48550/arxiv.2508.04089 · pith_short_12: GEMZFZD62ESF · pith_short_16: GEMZFZD62ESF6LGR · pith_short_8: GEMZFZD6

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/GEMZFZD62ESF6LGRW2DM6JHLUR \
  | 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: 311992e47ed1245f2cd1b686cf24eba463202e218af09d680b43e8565b280d5a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bbaef6d7028a55c31681aee5966ac489e043f7675dff4e17850560463b4f1c26",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2025-08-06T05:10:39Z",
    "title_canon_sha256": "948f3e4b0a68eb9435d0067feafc8f158f758add51f4100e419afb3a57cf4768"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.04089",
    "kind": "arxiv",
    "version": 1
  }
}