Pith Number

pith:NS3QGSPE

pith:2016:NS3QGSPEO4OLUU7M4IUIWE45UE

not attested not anchored not stored refs pending

Density estimates for $k$-impassable lattices of balls and general convex bodies in ${\Bbb R}^n$

E. Makai, H. Martini, Jr.

arxiv:1612.01307 v1 · 2016-12-05 · 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{NS3QGSPEO4OLUU7M4IUIWE45UE}

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	2026-05-18T00:55:52.966707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cb70349e4771cba53ece2288b139da107b56f58325777de24719b586bb77e6f

Aliases

arxiv: 1612.01307 · arxiv_version: 1612.01307v1 · doi: 10.48550/arxiv.1612.01307 · pith_short_12: NS3QGSPEO4OL · pith_short_16: NS3QGSPEO4OLUU7M · pith_short_8: NS3QGSPE

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/NS3QGSPEO4OLUU7M4IUIWE45UE \
  | 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: 6cb70349e4771cba53ece2288b139da107b56f58325777de24719b586bb77e6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "933f1323764dae9ef1b35cd85b1c0c6c2fe670403c541224cba4a8faab5bd651",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2016-12-05T11:03:54Z",
    "title_canon_sha256": "a435577f1399f6afec9a1b4c0160a7fbf7f61fc074213b1de221260a2d9e844d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01307",
    "kind": "arxiv",
    "version": 1
  }
}