Pith Number

pith:A6OWQGJD

pith:2026:A6OWQGJDYPS4J77SQY25SC2XFT

not attested not anchored not stored refs pending

Scalable Gaussian Processes for Integrated and Overlapping Measurements Via Augmented State Space Models

Daniel Foreman-Mackey, Jacob K. Luhn, Megan Bedell, Ryan A. Rubenzahl, Simo S\"arkk\"a, Soichiro Hattori, Will M. Farr

Augmenting state space models with a resetting integral state yields the exact Gaussian process posterior for integrated and overlapping measurements in linear time.

arxiv:2601.02527 v2 · 2026-01-05 · astro-ph.IM · astro-ph.EP · astro-ph.SR

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\usepackage{pith}
\pithnumber{A6OWQGJDYPS4J77SQY25SC2XFT}

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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

This construction yields exactly the same posterior as a fully integrated GP but in O(N) time on a CPU, and is parallelizable down to O(N/T + log T) on a GPU with T parallel workers.

C2weakest assumption

The augmentation with the integral state exactly reproduces the integrated measurement covariance without approximation or loss of the GP equivalence, which must hold for arbitrary exposure start and end times.

C3one line summary

Augmented state space models allow exact Gaussian process posteriors for integrated and overlapping measurements in O(N) time.

Receipt and verification

First computed	2026-05-18T03:10:11.414205Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

079d681923c3e5c4fff28635d90b572cf4b0c5439b3698725343a67157ed08e4

Aliases

arxiv: 2601.02527 · arxiv_version: 2601.02527v2 · doi: 10.48550/arxiv.2601.02527 · pith_short_12: A6OWQGJDYPS4 · pith_short_16: A6OWQGJDYPS4J77S · pith_short_8: A6OWQGJD

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/A6OWQGJDYPS4J77SQY25SC2XFT \
  | 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: 079d681923c3e5c4fff28635d90b572cf4b0c5439b3698725343a67157ed08e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf83ed37291ae3b7ff4ed11926cdd982154375bd5b33ccfa29b69a39411d52f7",
    "cross_cats_sorted": [
      "astro-ph.EP",
      "astro-ph.SR"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "astro-ph.IM",
    "submitted_at": "2026-01-05T20:00:50Z",
    "title_canon_sha256": "3ec231ef3c4846144fa320a7a54521baed33f5f79424e345152d2be10ee5aaa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.02527",
    "kind": "arxiv",
    "version": 2
  }
}