Pith Number

pith:BU2C4DHT

pith:2013:BU2C4DHTQWWN4TV5LHCXQMM3DJ

not attested not anchored not stored refs pending

On the topological minimality of unions of planes of arbitrary dimension

Xiangyu Liang

arxiv:1312.3489 v1 · 2013-12-12 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BU2C4DHTQWWN4TV5LHCXQMM3DJ}

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	2026-05-18T03:04:50.785405Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d342e0cf385acde4ebd59c578319b1a65fb63a0ab3633214b74985ad8761303

Aliases

arxiv: 1312.3489 · arxiv_version: 1312.3489v1 · doi: 10.48550/arxiv.1312.3489 · pith_short_12: BU2C4DHTQWWN · pith_short_16: BU2C4DHTQWWN4TV5 · pith_short_8: BU2C4DHT

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/BU2C4DHTQWWN4TV5LHCXQMM3DJ \
  | 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: 0d342e0cf385acde4ebd59c578319b1a65fb63a0ab3633214b74985ad8761303

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5de8d38358f29c014da2522fec6218eece5a3716d539a0291c7ebc2cb7a4913a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2013-12-12T13:59:02Z",
    "title_canon_sha256": "95e2508c0f9b08df0e61f0b02de91209b1172808435b1f09b3d6a795ebd6b170"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.3489",
    "kind": "arxiv",
    "version": 1
  }
}