Pith Number

pith:TLZZZPDA

pith:2024:TLZZZPDAHR2JSOU65C7L4HZLG4

not attested not anchored not stored refs pending

Gradient flows of $(K,N)$-convex functions with negative $N$

Chiara Rigoni, Lorenzo Dello Schiavo, Mattia Magnabosco

arxiv:2412.04574 v2 · 2024-12-05 · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TLZZZPDAHR2JSOU65C7L4HZLG4}

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	2026-05-25T02:01:01.952106Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9af39cbc603c74993a9ee8bebe1f2b371e1f3e48d28f958abed1ca6c234ac802

Aliases

arxiv: 2412.04574 · arxiv_version: 2412.04574v2 · doi: 10.48550/arxiv.2412.04574 · pith_short_12: TLZZZPDAHR2J · pith_short_16: TLZZZPDAHR2JSOU6 · pith_short_8: TLZZZPDA

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/TLZZZPDAHR2JSOU65C7L4HZLG4 \
  | 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: 9af39cbc603c74993a9ee8bebe1f2b371e1f3e48d28f958abed1ca6c234ac802

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d628cd5e38b661d41c04c64208f3593a8b3ac706b66f8b2b5f40414c6a42feb",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2024-12-05T19:39:52Z",
    "title_canon_sha256": "334068138240aae0ac74b44ceee6060e0c7699070325dab72f5755312f2ae470"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.04574",
    "kind": "arxiv",
    "version": 2
  }
}