Pith Number

pith:7CM2LL6A

pith:2010:7CM2LL6AELIKIAAN5PFIILUD4B

not attested not anchored not stored refs pending

Minimal time control of fed-batch processes with growth functions having several maxima

Alain Rapaport (Mistea - EPI MERE INRA/INRIA), Denis Dochain (Cesame)

arxiv:1010.4930 v1 · 2010-10-24 · 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{7CM2LL6AELIKIAAN5PFIILUD4B}

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	2026-05-18T04:38:49.795367Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f899a5afc022d0a4000debca842e83e04889ce36d6d8efede719767175953b8c

Aliases

arxiv: 1010.4930 · arxiv_version: 1010.4930v1 · doi: 10.48550/arxiv.1010.4930 · pith_short_12: 7CM2LL6AELIK · pith_short_16: 7CM2LL6AELIKIAAN · pith_short_8: 7CM2LL6A

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/7CM2LL6AELIKIAAN5PFIILUD4B \
  | 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: f899a5afc022d0a4000debca842e83e04889ce36d6d8efede719767175953b8c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d7a7aa0131822a76d7ed4d39b75aa82eb4c48eee6a27a4beffecbe28f95f0e2e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2010-10-24T05:30:13Z",
    "title_canon_sha256": "75d2159b05fa73c16851ae7326e1e13185c350d7ce7a3ac59379564f6649ce85"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.4930",
    "kind": "arxiv",
    "version": 1
  }
}