Pith Number

pith:2ATAMWH2

pith:2012:2ATAMWH2VK3SWE5FEANWQYVCFU

not attested not anchored not stored refs pending

On necessary boundary conditions for strictly optimal control in infinite horizon control problems

Dmitry Khlopin

arxiv:1212.6309 v1 · 2012-12-27 · 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{2ATAMWH2VK3SWE5FEANWQYVCFU}

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	2026-05-18T03:37:40.211636Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0260658faaab72b13a5201b6862a22d00f912942d75bfd02ae3c96b663c9c5b

Aliases

arxiv: 1212.6309 · arxiv_version: 1212.6309v1 · doi: 10.48550/arxiv.1212.6309 · pith_short_12: 2ATAMWH2VK3S · pith_short_16: 2ATAMWH2VK3SWE5F · pith_short_8: 2ATAMWH2

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/2ATAMWH2VK3SWE5FEANWQYVCFU \
  | 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: d0260658faaab72b13a5201b6862a22d00f912942d75bfd02ae3c96b663c9c5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "044b42912901d3d35474faf0770274612986b27e51b209c69f9eb3e96bbe2096",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-12-27T06:08:55Z",
    "title_canon_sha256": "e6b39ec42b1868fde601372d526183cf37b44dbace2a44ed6b4cd09b907b6493"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.6309",
    "kind": "arxiv",
    "version": 1
  }
}