Pith Number

pith:67PXVZHK

pith:2018:67PXVZHKQ5NUV6GK7B63KJX3SJ

not attested not anchored not stored refs pending

Growth on Two Limiting Essential Resources in a Self-Cycling Fermentor

Gail S. K. Wolkowicz, Lin Wang, Ting-Hao Hsu, Tyler Meadows

arxiv:1809.02550 v1 · 2018-09-07 · 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{67PXVZHKQ5NUV6GK7B63KJX3SJ}

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	2026-05-18T00:06:16.804469Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7df7ae4ea875b4af8caf87db526fb92622ee9062e654979eb9d2c0bbdda26b2

Aliases

arxiv: 1809.02550 · arxiv_version: 1809.02550v1 · doi: 10.48550/arxiv.1809.02550 · pith_short_12: 67PXVZHKQ5NU · pith_short_16: 67PXVZHKQ5NUV6GK · pith_short_8: 67PXVZHK

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/67PXVZHKQ5NUV6GK7B63KJX3SJ \
  | 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: f7df7ae4ea875b4af8caf87db526fb92622ee9062e654979eb9d2c0bbdda26b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "694b15c65d63def8d8fa551f28396960d5bbe1e5d285755dd2f07bc02bbc627c",
    "cross_cats_sorted": [
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2018-09-07T15:50:26Z",
    "title_canon_sha256": "41bcf964f873dd41e3718cca22e28c2f141bd1387932ac2780e459f6ff151a31"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.02550",
    "kind": "arxiv",
    "version": 1
  }
}