Pith Number

pith:YBPFZ3V7

pith:2013:YBPFZ3V76H4DD6XEI53NNKCWVB

not attested not anchored not stored refs pending

The p-Weak Gradient Depends on p

Gareth Speight, Simone Di Marino

arxiv:1311.4171 v2 · 2013-11-17 · 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{YBPFZ3V76H4DD6XEI53NNKCWVB}

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	2026-05-18T02:44:01.965125Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c05e5ceebff1f831fae44776d6a856a872590bb2068ffea68e93cb446201814d

Aliases

arxiv: 1311.4171 · arxiv_version: 1311.4171v2 · doi: 10.48550/arxiv.1311.4171 · pith_short_12: YBPFZ3V76H4D · pith_short_16: YBPFZ3V76H4DD6XE · pith_short_8: YBPFZ3V7

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/YBPFZ3V76H4DD6XEI53NNKCWVB \
  | 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: c05e5ceebff1f831fae44776d6a856a872590bb2068ffea68e93cb446201814d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f907442314dbbff4698d2812cefe0ed791be07ed889a964c9f46be69c1876756",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2013-11-17T15:44:06Z",
    "title_canon_sha256": "b15676d3b1680d9dab47171b64343c4479715844a6689631ff6496eb7ac86a22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.4171",
    "kind": "arxiv",
    "version": 2
  }
}