Pith Number

pith:MK5VDO4D

pith:2021:MK5VDO4DGEADEW5DT44LJWQ5Y5

not attested not anchored not stored refs pending

Macroscopic scalar curvature and codimension 2 width

Alexey Balitskiy, Hannah Alpert, Larry Guth

arxiv:2112.04594 v1 · 2021-12-08 · math.DG · 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{MK5VDO4DGEADEW5DT44LJWQ5Y5}

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.

Cited by

1 paper in Pith

1-Uryson width and covers

Receipt and verification

First computed	2026-07-05T07:01:23.361169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62bb51bb833100325ba39f38b4da1dc7683befb57e21fb41f8afb42fce4f6b0e

Aliases

arxiv: 2112.04594 · arxiv_version: 2112.04594v1 · doi: 10.48550/arxiv.2112.04594 · pith_short_12: MK5VDO4DGEAD · pith_short_16: MK5VDO4DGEADEW5D · pith_short_8: MK5VDO4D

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/MK5VDO4DGEADEW5DT44LJWQ5Y5 \
  | 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: 62bb51bb833100325ba39f38b4da1dc7683befb57e21fb41f8afb42fce4f6b0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b81ecdab170c857dcc819b2a524b4b67ff6e63317cd1a805e1d8356ed6d19fab",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2021-12-08T21:15:09Z",
    "title_canon_sha256": "408ee7580a9369c80060652e993111c6fb8b93445cc8986cb614e4c103f4a6ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.04594",
    "kind": "arxiv",
    "version": 1
  }
}