Pith Number

pith:XB6752RM

pith:2017:XB6752RM3JRSLQXLHFS2E36M3H

not attested not anchored not stored refs pending

Improvement on $2$-chains inside thin subsets of Euclidean spaces

Bochen Liu

arxiv:1709.06814 v2 · 2017-09-20 · math.CA · math.CO · 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{XB6752RM3JRSLQXLHFS2E36M3H}

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	2026-05-18T00:32:00.901495Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b87dfeea2cda6325c2eb3965a26fccd9fc14b15f9fa42967188b6f261049d239

Aliases

arxiv: 1709.06814 · arxiv_version: 1709.06814v2 · doi: 10.48550/arxiv.1709.06814 · pith_short_12: XB6752RM3JRS · pith_short_16: XB6752RM3JRSLQXL · pith_short_8: XB6752RM

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/XB6752RM3JRSLQXLHFS2E36M3H \
  | 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: b87dfeea2cda6325c2eb3965a26fccd9fc14b15f9fa42967188b6f261049d239

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80e079a32f7e31fd485468f1352490029bc041c60eb0c1fc7dd0dba97c29c889",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2017-09-20T11:10:21Z",
    "title_canon_sha256": "c81f01e4709d7270c593375c6a99289d130bd4586c737b585e842e4494dfa9a5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1709.06814",
    "kind": "arxiv",
    "version": 2
  }
}