Pith Number

pith:JVWPMLWU

pith:2026:JVWPMLWUNURCJYFVOY62KZWTUG

not attested not anchored not stored refs pending

The Geometry of Projection Heads: Conditioning, Invariance, and Collapse

Faris Chaudhry

arxiv:2605.17180 v1 · 2026-05-16 · 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{JVWPMLWUNURCJYFVOY62KZWTUG}

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	2026-05-20T00:03:43.717168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d6cf62ed46d2224e0b5763da566d3a1803911b635fb426717e067bb97804ade

Aliases

arxiv: 2605.17180 · arxiv_version: 2605.17180v1 · doi: 10.48550/arxiv.2605.17180 · pith_short_12: JVWPMLWUNURC · pith_short_16: JVWPMLWUNURCJYFV · pith_short_8: JVWPMLWU

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/JVWPMLWUNURCJYFVOY62KZWTUG \
  | 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: 4d6cf62ed46d2224e0b5763da566d3a1803911b635fb426717e067bb97804ade

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b973109550632c74276fab3fcd4ea10163cad85bf292e62db4b223573c0181c6",
    "cross_cats_sorted": [
      "math.OC",
      "stat.ML"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-16T22:32:05Z",
    "title_canon_sha256": "4772b851a2691f227c501a9320e2ee9af1c364bd4d4eaa1732708fca3b3f2d2f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17180",
    "kind": "arxiv",
    "version": 1
  }
}