Pith Number

pith:CWX5YODU

pith:2010:CWX5YODUVAVMSN6O6MPJF24BL2

not attested not anchored not stored refs pending

On tight spans and tropical polytopes for directed distances

Hiroshi Hirai, Shungo Koichi

arxiv:1004.0415 v1 · 2010-04-03 · 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{CWX5YODUVAVMSN6O6MPJF24BL2}

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	2026-05-18T03:33:12.258308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15afdc3874a82ac937cef31e92eb815e8bd307c50313682d96b3bf8fc1b37bff

Aliases

arxiv: 1004.0415 · arxiv_version: 1004.0415v1 · doi: 10.48550/arxiv.1004.0415 · pith_short_12: CWX5YODUVAVM · pith_short_16: CWX5YODUVAVMSN6O · pith_short_8: CWX5YODU

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/CWX5YODUVAVMSN6O6MPJF24BL2 \
  | 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: 15afdc3874a82ac937cef31e92eb815e8bd307c50313682d96b3bf8fc1b37bff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e5feac2c192ab2b0742fa009ec13a8162b39a268980c314034162785972a17d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2010-04-03T04:07:01Z",
    "title_canon_sha256": "59d80488999c53a9fcb0400947a747968eb22fbc7d67aea194aa58792d5c09b4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0415",
    "kind": "arxiv",
    "version": 1
  }
}