Pith Number

pith:2TK2MVQV

pith:2000:2TK2MVQV5G2OESHWQEHLYYJX64

not attested not anchored not stored refs pending

Output-input stability and minimum-phase nonlinear systems

A. Stephen Morse, Daniel Liberzon, Eduardo D. Sontag

arxiv:math/0006133 v2 · 2000-06-19 · math.OC · math.DS

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2TK2MVQV5G2OESHWQEHLYYJX64}

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	2026-05-18T00:58:26.452947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4d5a65615e9b4e248f6810ebc6137f729c899fac71d6b3e7daac0fdc8b0e6b5

Aliases

arxiv: math/0006133 · arxiv_version: math/0006133v2 · doi: 10.48550/arxiv.math/0006133 · pith_short_12: 2TK2MVQV5G2O · pith_short_16: 2TK2MVQV5G2OESHW · pith_short_8: 2TK2MVQV

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/2TK2MVQV5G2OESHWQEHLYYJX64 \
  | 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: d4d5a65615e9b4e248f6810ebc6137f729c899fac71d6b3e7daac0fdc8b0e6b5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4de2baae21c1f5a24dd4eed7cbb1ad842b3b0ccc89182d7aff7a7bbc8ae3e8b9",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "",
    "primary_cat": "math.OC",
    "submitted_at": "2000-06-19T17:24:20Z",
    "title_canon_sha256": "3680d9b21ddceaebafb7a3da53382f2a310b802e795a1b069837adf212e0a94c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0006133",
    "kind": "arxiv",
    "version": 2
  }
}