Pith Number

pith:QCTXK46Y

pith:2010:QCTXK46YHJQCRH7DK7TC3WWKFE

not attested not anchored not stored refs pending

A variational and symplectic framework for model-free control: preliminary results

Lo\"ic Michel

arxiv:1011.4237 v2 · 2010-11-18 · eess.SY · cs.SY · 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{QCTXK46YHJQCRH7DK7TC3WWKFE}

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	2026-06-03T23:06:43.883949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

80a77573d83a60289fe357e62ddaca290e39e1848465186f666dd56648cf2a45

Aliases

arxiv: 1011.4237 · arxiv_version: 1011.4237v2 · doi: 10.48550/arxiv.1011.4237 · pith_short_12: QCTXK46YHJQC · pith_short_16: QCTXK46YHJQCRH7D · pith_short_8: QCTXK46Y

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/QCTXK46YHJQCRH7DK7TC3WWKFE \
  | 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: 80a77573d83a60289fe357e62ddaca290e39e1848465186f666dd56648cf2a45

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d45ba7f73186fb5ee9637c60333edee58d6d5f7d43f4e9276d044cec9594ded4",
    "cross_cats_sorted": [
      "cs.SY",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2010-11-18T17:14:59Z",
    "title_canon_sha256": "dfc8c9e75f2424952c302d199fbb8ae6605ba00d64d31393b93e7d00907dea24"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.4237",
    "kind": "arxiv",
    "version": 2
  }
}