Pith Number

pith:5PBU3UBG

pith:2021:5PBU3UBG7ACUVBAJ3RZUT6WABI

not attested not anchored not stored refs pending

The Scaled Relative Graph of a Linear Operator

Richard Pates

arxiv:2106.05650 v2 · 2021-06-10 · 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{5PBU3UBG7ACUVBAJ3RZUT6WABI}

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.

Cited by

4 papers in Pith

Computable Characterisations of Scaled Relative Graphs of Closed Operators

Scaled Relative Graphs in Normed Spaces

Scaled Graph Containment for Feedback Stability: Soft-Hard Equivalence and Conic Regions

Symmetry Is Almost All You Need: Robust Stability with Uncertainty Induced by Symmetric SRG Regions

Receipt and verification

First computed	2026-07-05T03:03:08.716918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebc34dd026f8054a8409dc7349fac00a06d5a9d4a5a8b1b2fe3b7f69b7bc2a12

Aliases

arxiv: 2106.05650 · arxiv_version: 2106.05650v2 · doi: 10.48550/arxiv.2106.05650 · pith_short_12: 5PBU3UBG7ACU · pith_short_16: 5PBU3UBG7ACUVBAJ · pith_short_8: 5PBU3UBG

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/5PBU3UBG7ACUVBAJ3RZUT6WABI \
  | 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: ebc34dd026f8054a8409dc7349fac00a06d5a9d4a5a8b1b2fe3b7f69b7bc2a12

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f45a3dea6b82d289d22588ea3a6a8a099e907813bb1369090ebdcdf77055927",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2021-06-10T10:45:38Z",
    "title_canon_sha256": "d0742db4123f60b124f19cd028fb9ee8b2a835626e01b3749060b302a428d2b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2106.05650",
    "kind": "arxiv",
    "version": 2
  }
}