Pith Number

pith:H2R45JPH

pith:2012:H2R45JPHM4MDS76TCPGJWBRMON

not attested not anchored not stored refs pending

Optimal growth for linear processes with affine control

Pierre Gabriel (LJLL), Vincent Calvez (UMPA-ENSL)

arxiv:1203.5189 v1 · 2012-03-23 · math.AP · 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{H2R45JPHM4MDS76TCPGJWBRMON}

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	2026-05-18T03:59:26.637517Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ea3cea5e76718397fd313cc9b062c7378fd3a7a7daa060d9b5bdc149542b977

Aliases

arxiv: 1203.5189 · arxiv_version: 1203.5189v1 · doi: 10.48550/arxiv.1203.5189 · pith_short_12: H2R45JPHM4MD · pith_short_16: H2R45JPHM4MDS76T · pith_short_8: H2R45JPH

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/H2R45JPHM4MDS76TCPGJWBRMON \
  | 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: 3ea3cea5e76718397fd313cc9b062c7378fd3a7a7daa060d9b5bdc149542b977

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bcb6cba1db59af9e119249195c6a72fd4b0a2c4e2e93c2dae1c45b67c1204c1d",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-03-23T07:15:06Z",
    "title_canon_sha256": "d0a7ebd6667b8015c26b094eec8e4e20af9dbbac13465d4ff6fa0ff585f9ac4f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.5189",
    "kind": "arxiv",
    "version": 1
  }
}