Pith Number

pith:BDP5V67M

pith:2025:BDP5V67MELZEENC5PGY5JWBVYO

not attested not anchored not stored refs pending

KPFlow: An Operator Perspective on Dynamic Collapse Under Gradient Descent Training of Recurrent Networks

Eli Shlizerman, Eric Shea-Brown, James Hazelden, Laura Driscoll

arxiv:2507.06381 v1 · 2025-07-08 · cs.LG · cs.AI · math.DS · q-bio.NC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BDP5V67MELZEENC5PGY5JWBVYO}

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	2026-07-05T11:34:14.774255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

08dfdafbec22f242345d79b1d4d835c380f4c37978bf99e268588e2c728d802c

Aliases

arxiv: 2507.06381 · arxiv_version: 2507.06381v1 · doi: 10.48550/arxiv.2507.06381 · pith_short_12: BDP5V67MELZE · pith_short_16: BDP5V67MELZEENC5 · pith_short_8: BDP5V67M

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/BDP5V67MELZEENC5PGY5JWBVYO \
  | 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: 08dfdafbec22f242345d79b1d4d835c380f4c37978bf99e268588e2c728d802c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e11492ad12cd7b1ff5fad79b82bfdd325011f224fa559bf4eb4eb73fbf220509",
    "cross_cats_sorted": [
      "cs.AI",
      "math.DS",
      "q-bio.NC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-07-08T20:33:15Z",
    "title_canon_sha256": "d952646ee7e6ab25c72d7e2f913630c62c22fac6e4c39a48a8334ba33f9f0f88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.06381",
    "kind": "arxiv",
    "version": 1
  }
}