Pith Number

pith:WPUE7FJ4

pith:2026:WPUE7FJ4CTE6UBLP5B25F76XSM

not attested not anchored not stored refs pending

Aggregation as a Double-Edged Sword: Fear, Allee Effects, and Finite-Time Collapse

Eric M. Takyi, Kwadwo Antwi-Fordjour

arxiv:2606.17586 v1 · 2026-06-16 · q-bio.PE · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WPUE7FJ4CTE6UBLP5B25F76XSM}

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	2026-06-19T16:10:16.607612Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3e84f953c14c9ea056fe875d2ffd79333b273fe0963872f32d78a23fab8ca79

Aliases

arxiv: 2606.17586 · arxiv_version: 2606.17586v1 · doi: 10.48550/arxiv.2606.17586 · pith_short_12: WPUE7FJ4CTE6 · pith_short_16: WPUE7FJ4CTE6UBLP · pith_short_8: WPUE7FJ4

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/WPUE7FJ4CTE6UBLP5B25F76XSM \
  | 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: b3e84f953c14c9ea056fe875d2ffd79333b273fe0963872f32d78a23fab8ca79

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44fa9448a34ff05e278ba7e2b55dabd02cd98b3b09a1079b5a8a778ebc22c04f",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "q-bio.PE",
    "submitted_at": "2026-06-16T06:48:51Z",
    "title_canon_sha256": "74e1e5cc0e872f8359956692ceeeecbce537a1c81cd4fe2a52c523980ea0c88c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.17586",
    "kind": "arxiv",
    "version": 1
  }
}