Pith Number

pith:CACRIYSZ

pith:2006:CACRIYSZFUCE32LNFIBWSBUTGC

not attested not anchored not stored refs pending

Singular trajectories of control-affine systems

Emmanuel Tr\'elat (MAPMO), Fr\'ed\'eric Jean, Yacine Chitour (LSS)

arxiv:math/0607455 v1 · 2006-07-19 · 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{CACRIYSZFUCE32LNFIBWSBUTGC}

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	2026-05-18T01:08:49.995383Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

10051462592d044de96d2a03690693308f79709ed7eb4140543835a9454c1db1

Aliases

arxiv: math/0607455 · arxiv_version: math/0607455v1 · doi: 10.48550/arxiv.math/0607455 · pith_short_12: CACRIYSZFUCE · pith_short_16: CACRIYSZFUCE32LN · pith_short_8: CACRIYSZ

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/CACRIYSZFUCE32LNFIBWSBUTGC \
  | 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: 10051462592d044de96d2a03690693308f79709ed7eb4140543835a9454c1db1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d48909aa5caf3eb93a4d567ff27b26d871035888efa6751207ed8f9efdcbbff0",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OC",
    "submitted_at": "2006-07-19T09:30:32Z",
    "title_canon_sha256": "068fb92447159da5d0eaafbf35cdaa81f4d67ae17da7c53b0bad585b3e78ffad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0607455",
    "kind": "arxiv",
    "version": 1
  }
}