Pith Number

pith:YRLFQY7M

pith:2009:YRLFQY7MFIWN6UOZYQDRASRH2P

not attested not anchored not stored refs pending

Pontryagin Maximum Principle - a generalization

Janusz Grabowski, Michal Jozwikowski

arxiv:0905.2767 v2 · 2009-05-17 · math.OC · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YRLFQY7MFIWN6UOZYQDRASRH2P}

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	2026-05-18T03:21:10.974014Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c4565863ec2a2cdf51d9c407104a27d3d572eb2458efe98ca7370353e8eaa9f3

Aliases

arxiv: 0905.2767 · arxiv_version: 0905.2767v2 · doi: 10.48550/arxiv.0905.2767 · pith_short_12: YRLFQY7MFIWN · pith_short_16: YRLFQY7MFIWN6UOZ · pith_short_8: YRLFQY7M

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/YRLFQY7MFIWN6UOZYQDRASRH2P \
  | 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: c4565863ec2a2cdf51d9c407104a27d3d572eb2458efe98ca7370353e8eaa9f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "130df6723a115a7c141a0891f754efbc090f9c0dd8556969a81d32d11d308f0d",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-05-17T20:16:21Z",
    "title_canon_sha256": "3654013159fd9a9b9b2b7b625c8cd3bd6d98475dbe1c744f2d0582d13404f141"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.2767",
    "kind": "arxiv",
    "version": 2
  }
}