Pith Number

pith:DU42JWDL

pith:2025:DU42JWDLPRDFOIYPJUMD7ROLEI

not attested not anchored not stored refs pending

Latent-Space Mean-Field Theory for Deep BitNet-like Training: Constrained Gradient Flows with Smooth Quantization and STE Limits

Dongseok Lee, Dongwon Kim

arxiv:2509.00133 v1 · 2025-08-29 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DU42JWDLPRDFOIYPJUMD7ROLEI}

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	2026-07-05T12:02:09.958989Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d39a4d86b7c4657230f4d183fc5cb22032639a74e3ab3777ffb0846e9439b0c

Aliases

arxiv: 2509.00133 · arxiv_version: 2509.00133v1 · doi: 10.48550/arxiv.2509.00133 · pith_short_12: DU42JWDLPRDF · pith_short_16: DU42JWDLPRDFOIYP · pith_short_8: DU42JWDL

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/DU42JWDLPRDFOIYPJUMD7ROLEI \
  | 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: 1d39a4d86b7c4657230f4d183fc5cb22032639a74e3ab3777ffb0846e9439b0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a8ee65c5aa09b138789da88d125ac96699e213eb21d3758804af62b071fb818",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-08-29T14:17:05Z",
    "title_canon_sha256": "938f4a4cd9db6262bfe71ca3e0afcd30eab16b21ff5354c6e474a98fa93284f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.00133",
    "kind": "arxiv",
    "version": 1
  }
}