Pith Number

pith:J3CGKQGQ

pith:2018:J3CGKQGQXL326SWMZ6EYZPTDAN

not attested not anchored not stored refs pending

ABP inequalities for singular submanifolds of bounded mean curvature

Mario Santilli

arxiv:1809.02198 v1 · 2018-09-06 · math.AP · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{J3CGKQGQXL326SWMZ6EYZPTDAN}

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	2026-05-18T00:06:17.683740Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4ec46540d0baf7af4acccf898cbe630363b2ddd62ed6e96cb833795609e11a6c

Aliases

arxiv: 1809.02198 · arxiv_version: 1809.02198v1 · doi: 10.48550/arxiv.1809.02198 · pith_short_12: J3CGKQGQXL32 · pith_short_16: J3CGKQGQXL326SWM · pith_short_8: J3CGKQGQ

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/J3CGKQGQXL326SWMZ6EYZPTDAN \
  | 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: 4ec46540d0baf7af4acccf898cbe630363b2ddd62ed6e96cb833795609e11a6c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bdf78f00a5ad52069cdba7ef0054e507f0e251591fbf9033539aa13731fa1c14",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-09-06T19:59:19Z",
    "title_canon_sha256": "fdfbcdd932d6c903c675c25899a42c000a69660d147ca5e3812c78b598753822"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1809.02198",
    "kind": "arxiv",
    "version": 1
  }
}