Pith Number

pith:A42GSNVX

pith:2026:A42GSNVXEYC77CK5EJ4GJDQD6H

not attested not anchored not stored refs pending

Fisher Widths: Local Learning Geometry and Anisotropic Recovery

Vu Khac Ky

arxiv:2607.20578 v1 · 2026-07-22 · cs.LG · math.ST · stat.ML · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A42GSNVXEYC77CK5EJ4GJDQD6H}

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	2026-07-24T00:23:23.559338Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07346936b72605ff895d2278648e03f1d627d8364898e908adf832c8d6ba886c

Aliases

arxiv: 2607.20578 · arxiv_version: 2607.20578v1 · doi: 10.48550/arxiv.2607.20578 · pith_short_12: A42GSNVXEYC7 · pith_short_16: A42GSNVXEYC77CK5 · pith_short_8: A42GSNVX

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/A42GSNVXEYC77CK5EJ4GJDQD6H \
  | 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: 07346936b72605ff895d2278648e03f1d627d8364898e908adf832c8d6ba886c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ddb4ea93d9cb0f8e67e587ba74a7d27f2dcbb6802d68dfcc275c56d95af4f21f",
    "cross_cats_sorted": [
      "math.ST",
      "stat.ML",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-22T10:07:03Z",
    "title_canon_sha256": "94d5d9fc39a2d39d8690083e357c68aa2f7b05560165a175014564ca940d4760"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.20578",
    "kind": "arxiv",
    "version": 1
  }
}