Pith Number

pith:LZSCXM54

pith:2026:LZSCXM5465UPZVUPLE4XC3M2XR

not attested not anchored not stored refs pending

A Counterexample to Fourier Alignment in Single-Neuron Modular Addition

Gautam Neelakantan Memana

arxiv:2608.04451 v1 · 2026-08-05 · math.OC · cs.LG · cs.NE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LZSCXM5465UPZVUPLE4XC3M2XR}

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	2026-08-06T01:35:30.445957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e642bb3bcf768fcd68f5939716d9abc665710add2a7268c99bde4ba67f06d8b

Aliases

arxiv: 2608.04451 · arxiv_version: 2608.04451v1 · doi: 10.48550/arxiv.2608.04451 · pith_short_12: LZSCXM5465UP · pith_short_16: LZSCXM5465UPZVUP · pith_short_8: LZSCXM54

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/LZSCXM5465UPZVUPLE4XC3M2XR \
  | 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: 5e642bb3bcf768fcd68f5939716d9abc665710add2a7268c99bde4ba67f06d8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "509911e0a54331ecb070e0385fd072887cf9d78bdd60db3bb7796e01c82e4627",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-08-05T04:56:53Z",
    "title_canon_sha256": "57f2f87bd9048e77a328207fe4a71463992da8c1219a909e15ce3c5615d6151f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04451",
    "kind": "arxiv",
    "version": 1
  }
}