Pith Number

pith:IXUFWQT6

pith:2014:IXUFWQT6GAQDYSTPXLBRS6IZXQ

not attested not anchored not stored refs pending

Three laws of feedback systems: entropy rate never decreases, generalized Bode integral, absolute lower bound in variance minimization, Gaussianity-whiteness measure (joint Shannon-Wiener entropy), Gaussianing-whitening control, and beyond

Song Fang

arxiv:1410.5192 v6 · 2014-10-20 · cs.SY · cs.IT · math.IT · 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{IXUFWQT6GAQDYSTPXLBRS6IZXQ}

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	2026-05-18T02:30:54.670926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

45e85b427e30203c4a6fbac3197919bc207380c4d61aca9b7fc2a44a200e0905

Aliases

arxiv: 1410.5192 · arxiv_version: 1410.5192v6 · doi: 10.48550/arxiv.1410.5192 · pith_short_12: IXUFWQT6GAQD · pith_short_16: IXUFWQT6GAQDYSTP · pith_short_8: IXUFWQT6

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/IXUFWQT6GAQDYSTPXLBRS6IZXQ \
  | 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: 45e85b427e30203c4a6fbac3197919bc207380c4d61aca9b7fc2a44a200e0905

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0bf4ad95edae0d6708d676a5552fc3ac4c0fc83b2981dec4fa3ef252f485dd5",
    "cross_cats_sorted": [
      "cs.IT",
      "math.IT",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.SY",
    "submitted_at": "2014-10-20T08:37:56Z",
    "title_canon_sha256": "1d6b7aa6769d3993314000f5f19a7f6f89e5c3887ab0b3ce97b740af21c4cbeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1410.5192",
    "kind": "arxiv",
    "version": 6
  }
}