Pith Number

pith:OZ4GWXCU

pith:2010:OZ4GWXCUGVYCGFWG4OK4LO7O77

not attested not anchored not stored refs pending

On sets of directions determined by subsets of ${\Bbb R}^d$

Alex Iosevich, Mihalis Mourgoglou, Steven Senger

arxiv:1009.4169 v2 · 2010-09-21 · math.CA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZ4GWXCUGVYCGFWG4OK4LO7O77}

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	2026-05-18T04:25:13.104413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76786b5c5435702316c6e395c5bbeefffc1118643f54dba67eab75283c26c5ec

Aliases

arxiv: 1009.4169 · arxiv_version: 1009.4169v2 · doi: 10.48550/arxiv.1009.4169 · pith_short_12: OZ4GWXCUGVYC · pith_short_16: OZ4GWXCUGVYCGFWG · pith_short_8: OZ4GWXCU

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/OZ4GWXCUGVYCGFWG4OK4LO7O77 \
  | 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: 76786b5c5435702316c6e395c5bbeefffc1118643f54dba67eab75283c26c5ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "27465e90e05fcdec277e874b6848a953b74647cc4ac0c393beb1a519db53c606",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2010-09-21T18:24:13Z",
    "title_canon_sha256": "526997461f08651524f7d355974a32d1bcc8325111b142f2aba62e6ebe2854e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.4169",
    "kind": "arxiv",
    "version": 2
  }
}