Pith Number

pith:M4TS7NVT

pith:2018:M4TS7NVTNFDUXYUKV3D5ZKNELW

not attested not anchored not stored refs pending

The sphere covering inequality and its dual

Amir Moradifam, Changfeng Gui, Fengbo Hang

arxiv:1812.09994 v1 · 2018-12-24 · 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{M4TS7NVTNFDUXYUKV3D5ZKNELW}

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	2026-05-17T23:57:08.156259Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67272fb6b369474be28aaec7dca9a45d9b36669679680a3ccb2164d28da3da00

Aliases

arxiv: 1812.09994 · arxiv_version: 1812.09994v1 · doi: 10.48550/arxiv.1812.09994 · pith_short_12: M4TS7NVTNFDU · pith_short_16: M4TS7NVTNFDUXYUK · pith_short_8: M4TS7NVT

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/M4TS7NVTNFDUXYUKV3D5ZKNELW \
  | 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: 67272fb6b369474be28aaec7dca9a45d9b36669679680a3ccb2164d28da3da00

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a46e8f0c9fbcefaef2d52b67e2cf3b8831d8b53ab24220e297aa61c9be44e879",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2018-12-24T22:41:08Z",
    "title_canon_sha256": "20c49604b87329e21200242055ea5a2c6c73c9ce9a0f74f612b84eb16f2d111d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1812.09994",
    "kind": "arxiv",
    "version": 1
  }
}