Pith Number

pith:F4US5VX7

pith:2026:F4US5VX74UHWUWG74SVA7GD4P4

not attested not anchored not stored refs pending

M+Adam: Low-Precision Training via Additive-Multiplicative Optimization

Anima Anandkumar, Mads Toftrup, Sebastian Loeschcke, Xiaoyuan Liang

arxiv:2607.10611 v1 · 2026-07-12 · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{F4US5VX74UHWUWG74SVA7GD4P4}

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	2026-07-14T01:21:23.859382Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f292ed6ffe50f6a58dfe4aa0f987c7f1da52da63678873fccc63a727692f37b

Aliases

arxiv: 2607.10611 · arxiv_version: 2607.10611v1 · doi: 10.48550/arxiv.2607.10611 · pith_short_12: F4US5VX74UHW · pith_short_16: F4US5VX74UHWUWG7 · pith_short_8: F4US5VX7

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/F4US5VX74UHWUWG74SVA7GD4P4 \
  | 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: 2f292ed6ffe50f6a58dfe4aa0f987c7f1da52da63678873fccc63a727692f37b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55583e56014e63b0a234e543d74ac809512ce4b17581b29ba17cfc4171c00403",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-12T07:15:47Z",
    "title_canon_sha256": "6bfb0e24bb36ab5c43ada5f4b35c7b741e06e8d3728ebd2a471fcc8aa29204cd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10611",
    "kind": "arxiv",
    "version": 1
  }
}