Pith Number

pith:IRHPCOID

pith:2025:IRHPCOIDHMHNIEPH4UIV6XM5XP

not attested not anchored not stored refs resolved

Identification with Orthogonal Basis Functions: Convergence Speed, Asymptotic Bias, and Rate-Optimal Pole Selection

Jiayun Li, Jie Chen, Yilin Mo, Yiwen Lu

Selecting Tsuji points for model poles lets orthogonal basis function identification reach the lowest possible asymptotic H2 bias for LTI systems.

arxiv:2512.21096 v3 · 2025-12-24 · 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{IRHPCOIDHMHNIEPH4UIV6XM5XP}

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.

Claims

C1strongest claim

The pole selection algorithm is asymptotically optimal, achieving the fundamental lower bound on the identification bias. The asymptotic identification bias decreases exponentially with the number of basis functions, with the rate of decrease governed by the hyperbolic Chebyshev constant.

C2weakest assumption

The true system is linear time-invariant with poles inside the unit disk, and the H2 bias bound depends only on the locations of the true and model poles without additional unmodeled dynamics or noise assumptions that would invalidate the worst-case minimization.

C3one line summary

OBF-based system identification achieves exponentially decaying asymptotic bias when poles are chosen as Tsuji points, attaining the fundamental lower bound on H2 identification error.

References

51 extracted · 51 resolved · 0 Pith anchors

[1] L. Ljung, “System identification,” pp. 163–173, 1998 1998

[2] H. Madsen,Time Series Analysis. Chapman & Hall/CRC, 2008 2008

[3] A. Lindquist and G. Picci,Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification. Springer Verlag, 2015 2015

[4] From circuit theory to system theory, 1962

[5] Linear stochastic filtering-reappraisal and outlook, 1965

Receipt and verification

First computed	2026-05-17T23:39:00.387564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

444ef139033b0ed411e7e5115f5d9dbbff539d63dcc1a7f894da4b0d15b598ec

Aliases

arxiv: 2512.21096 · arxiv_version: 2512.21096v3 · doi: 10.48550/arxiv.2512.21096 · pith_short_12: IRHPCOIDHMHN · pith_short_16: IRHPCOIDHMHNIEPH · pith_short_8: IRHPCOID

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/IRHPCOIDHMHNIEPH4UIV6XM5XP \
  | 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: 444ef139033b0ed411e7e5115f5d9dbbff539d63dcc1a7f894da4b0d15b598ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69a7e59c1595e3a0f7743642d214e923fcead000b264e2bcf82034aa996009af",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-12-24T10:35:37Z",
    "title_canon_sha256": "b5b7429218331a46118732837bd176119b498be637d29134d6ce1fdd50f9be00"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.21096",
    "kind": "arxiv",
    "version": 3
  }
}