Pith Number

pith:DGC7Y54Y

pith:2009:DGC7Y54YPSMISXALS6WCROGW5P

not attested not anchored not stored refs pending

A Short Proof of the Pontryagin Maximum Principle on Manifolds

Dong Eui Chang

arxiv:0905.1888 v2 · 2009-05-12 · 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{DGC7Y54YPSMISXALS6WCROGW5P}

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	2026-05-18T04:19:43.971044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1985fc77987c98895c0b97ac28b8d6ebc52220d5c384b9acce1a826877228b7e

Aliases

arxiv: 0905.1888 · arxiv_version: 0905.1888v2 · doi: 10.48550/arxiv.0905.1888 · pith_short_12: DGC7Y54YPSMI · pith_short_16: DGC7Y54YPSMISXAL · pith_short_8: DGC7Y54Y

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/DGC7Y54YPSMISXALS6WCROGW5P \
  | 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: 1985fc77987c98895c0b97ac28b8d6ebc52220d5c384b9acce1a826877228b7e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5c81c1d144d7f6b409014e3760c6b3f066f9c9150e69fe8e887c8fa74150d7e8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2009-05-12T15:49:20Z",
    "title_canon_sha256": "ed930a85359367871ba6e4988ce1555eab362db6f89a9c683b6fe7395ddded43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.1888",
    "kind": "arxiv",
    "version": 2
  }
}