Pith Number

pith:V6YDHJHN

pith:2026:V6YDHJHNH65Z7QW46BPLS5HII6

not attested not anchored not stored refs pending

An Improved Analysis of the Last Iterate of the SubGradient Method in the Plane

Andrea Paudice, Guglielmo Beretta, Roberto Colomboni, Tommaso Cesari

arxiv:2607.15980 v1 · 2026-07-17 · 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{V6YDHJHNH65Z7QW46BPLS5HII6}

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	2026-07-20T02:19:23.923974Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

afb033a4ed3fbb9fc2dcf05eb974e847af572d96263adfa4f5045e79ea930f2d

Aliases

arxiv: 2607.15980 · arxiv_version: 2607.15980v1 · doi: 10.48550/arxiv.2607.15980 · pith_short_12: V6YDHJHNH65Z · pith_short_16: V6YDHJHNH65Z7QW4 · pith_short_8: V6YDHJHN

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/V6YDHJHNH65Z7QW46BPLS5HII6 \
  | 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: afb033a4ed3fbb9fc2dcf05eb974e847af572d96263adfa4f5045e79ea930f2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "97edc0fa9e4e393ba7231ba6de319a3ceec784cc3b01b05d9279920543d6ea7e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-07-17T14:12:45Z",
    "title_canon_sha256": "012bdce8cf7fd7c6a0482b04981b5d0fba593b14aa8e3c8f78d67d1b359d6ad2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.15980",
    "kind": "arxiv",
    "version": 1
  }
}