Pith Number

pith:CS6P6B7B

pith:2025:CS6P6B7BQPWZDHQEHVCAAZVEJ3

not attested not anchored not stored refs pending

The continuous version of the generalized exchange-driven growth model

Fernando P. da Costa, Jo\~ao T. Pinto, Prasanta K. Barik, Rafael Sasportes

arxiv:2509.01316 v1 · 2025-09-01 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CS6P6B7BQPWZDHQEHVCAAZVEJ3}

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	2026-07-05T12:02:58.157336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4

Aliases

arxiv: 2509.01316 · arxiv_version: 2509.01316v1 · doi: 10.48550/arxiv.2509.01316 · pith_short_12: CS6P6B7BQPWZ · pith_short_16: CS6P6B7BQPWZDHQE · pith_short_8: CS6P6B7B

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/CS6P6B7BQPWZDHQEHVCAAZVEJ3 \
  | 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: 14bcff07e183ed919e043d440066a44eea49d32359337d532908673d441555e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "080e1c9fdb22870282323d4e779f956bef9be18657109864279f2279717e1115",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-09-01T10:01:12Z",
    "title_canon_sha256": "cabad1afc5c4c0e6de34c7fdd81263b63a114586bab3d5e5aba4c801ae862b77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.01316",
    "kind": "arxiv",
    "version": 1
  }
}