Pith Number

pith:WPNYPYV3

pith:2026:WPNYPYV3S54W3VBMUVYADRTUBB

not attested not anchored not stored refs pending

Tipping the Balance: Allee Thresholds, Saddle-Node Bifurcations, and Optimal Sterile-Male Release Strategies for Anopheles Mosquitoes

Abba Gumel, C. Alex Safsten

arxiv:2606.17125 v1 · 2026-06-15 · q-bio.PE · math.DS · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPNYPYV3S54W3VBMUVYADRTUBB}

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	2026-06-19T16:10:03.757200Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3db87e2bb97796dd42ca57001c6740860e1f698f074c0cbcccf591d7544a738

Aliases

arxiv: 2606.17125 · arxiv_version: 2606.17125v1 · doi: 10.48550/arxiv.2606.17125 · pith_short_12: WPNYPYV3S54W · pith_short_16: WPNYPYV3S54W3VBM · pith_short_8: WPNYPYV3

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/WPNYPYV3S54W3VBMUVYADRTUBB \
  | 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: b3db87e2bb97796dd42ca57001c6740860e1f698f074c0cbcccf591d7544a738

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f48b8d926bfce5ac04c6013ddbfddd4f7aa4ed5460d27b5ffdd73dfb47a826e",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2026-06-15T14:56:48Z",
    "title_canon_sha256": "bf87140d5d785d311794255007d66238873c2487f5986a867d0a0383a17ce088"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17125",
    "kind": "arxiv",
    "version": 1
  }
}