Pith Number

pith:YATUSZKT

pith:2026:YATUSZKTMSRZN4DAKMSIGCWJKB

not attested not anchored not stored refs pending

Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability

Pierre Marion

arxiv:2606.18080 v1 · 2026-06-16 · 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{YATUSZKTMSRZN4DAKMSIGCWJKB}

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	2026-06-19T16:10:47.994648Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c02749655364a396f0605324830ac9507af8b5afa9424da3d57392792090a7f6

Aliases

arxiv: 2606.18080 · arxiv_version: 2606.18080v1 · doi: 10.48550/arxiv.2606.18080 · pith_short_12: YATUSZKTMSRZ · pith_short_16: YATUSZKTMSRZN4DA · pith_short_8: YATUSZKT

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/YATUSZKTMSRZN4DAKMSIGCWJKB \
  | 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: c02749655364a396f0605324830ac9507af8b5afa9424da3d57392792090a7f6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4186dcc38651c0d3aa325957ea974d2690772ca79adc55c3849a29d0a8b9a733",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-16T15:45:47Z",
    "title_canon_sha256": "4637b2cf86a781af97ff111a3bf512ec396e190d34380f368359eeac05f34af2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.18080",
    "kind": "arxiv",
    "version": 1
  }
}