Pith Number

pith:GTD5WN2P

pith:2026:GTD5WN2P7WO4LBGXENUFMPQSXA

not attested not anchored not stored refs pending

No Subspace to Track: Non-Identifiability and Optimizer State in Low-Rank Training

Noel Thomas

arxiv:2607.05872 v1 · 2026-07-07 · cs.LG · math.OC · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTD5WN2P7WO4LBGXENUFMPQSXA}

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	2026-07-08T01:18:48.876842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34c7db374ffd9dc584d72368563e12b82d04c46ab4a91504cd9015c528f45b4c

Aliases

arxiv: 2607.05872 · arxiv_version: 2607.05872v1 · doi: 10.48550/arxiv.2607.05872 · pith_short_12: GTD5WN2P7WO4 · pith_short_16: GTD5WN2P7WO4LBGX · pith_short_8: GTD5WN2P

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/GTD5WN2P7WO4LBGXENUFMPQSXA \
  | 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: 34c7db374ffd9dc584d72368563e12b82d04c46ab4a91504cd9015c528f45b4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9362df9b848e2314b63bfa040136824b753bc66dedd4fb97ddc620e692c99cea",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-07T06:06:04Z",
    "title_canon_sha256": "f40c49ecbfd56ae9f2988dcabb5da72ee4b522222399856747736918b6e7f3c6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.05872",
    "kind": "arxiv",
    "version": 1
  }
}