Pith Number

pith:VD4MOPPH

pith:2026:VD4MOPPHQG7VBJCHSFGEFA34TE

not attested not anchored not stored refs pending

Downward conditional monotonicity gives survival and extinction for contact processes in random environments

Joseph P. Stover

arxiv:2606.10257 v1 · 2026-06-08 · 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{VD4MOPPHQG7VBJCHSFGEFA34TE}

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	2026-06-10T01:09:02.907630Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8f8c73de781bf50a447914c42837c9932a442c243099ce92620f87c619a2fbd

Aliases

arxiv: 2606.10257 · arxiv_version: 2606.10257v1 · doi: 10.48550/arxiv.2606.10257 · pith_short_12: VD4MOPPHQG7V · pith_short_16: VD4MOPPHQG7VBJCH · pith_short_8: VD4MOPPH

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/VD4MOPPHQG7VBJCHSFGEFA34TE \
  | 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: a8f8c73de781bf50a447914c42837c9932a442c243099ce92620f87c619a2fbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2fe37819e02fde92a325e7f03d5119b2a3e2a3e6e787085d0637180b30691b9f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-06-08T23:56:24Z",
    "title_canon_sha256": "08cf9f8a1d0db6c8d0dae803b7c464990528500f99bac8a9af54693fe128bd40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.10257",
    "kind": "arxiv",
    "version": 1
  }
}