Pith Number

pith:4IFSE6TS

pith:2012:4IFSE6TS66R3Y422S7LWX73HPP

not attested not anchored not stored refs pending

Noether's Symmetry Theorem for Variational and Optimal Control Problems with Time Delay

Delfim F. M. Torres, Gastao S. F. Frederico

arxiv:1203.3656 v1 · 2012-03-16 · math.DS · math.CA · 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{4IFSE6TS66R3Y422S7LWX73HPP}

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	2026-05-18T03:50:35.351453Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e20b227a72f7a3bc735a97d76bff677bc1625935646d3283ffd9101a5795fc6c

Aliases

arxiv: 1203.3656 · arxiv_version: 1203.3656v1 · doi: 10.48550/arxiv.1203.3656 · pith_short_12: 4IFSE6TS66R3 · pith_short_16: 4IFSE6TS66R3Y422 · pith_short_8: 4IFSE6TS

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/4IFSE6TS66R3Y422S7LWX73HPP \
  | 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: e20b227a72f7a3bc735a97d76bff677bc1625935646d3283ffd9101a5795fc6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f220387bd34c3790b87b215ab996d636608e2ae3ee57d792e689588ba1a83c93",
    "cross_cats_sorted": [
      "math.CA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-03-16T10:19:49Z",
    "title_canon_sha256": "443a0f9e3a3b940becef289f53089275b07351e978ea5a952051b881a7b747de"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.3656",
    "kind": "arxiv",
    "version": 1
  }
}