Pith Number

pith:XPBMWTUH

pith:2010:XPBMWTUH2YZ2BGRKKXAAYMM7J3

not attested not anchored not stored refs pending

On macroscopic dimension of rationally essential manifolds

Alexander Dranishnikov

arxiv:1005.0424 v1 · 2010-05-04 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XPBMWTUH2YZ2BGRKKXAAYMM7J3}

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	2026-05-18T02:38:18.542661Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bbc2cb4e87d633a09a2a55c00c319f4ec34ed991ac0067486451449f3c28d07b

Aliases

arxiv: 1005.0424 · arxiv_version: 1005.0424v1 · doi: 10.48550/arxiv.1005.0424 · pith_short_12: XPBMWTUH2YZ2 · pith_short_16: XPBMWTUH2YZ2BGRK · pith_short_8: XPBMWTUH

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/XPBMWTUH2YZ2BGRKKXAAYMM7J3 \
  | 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: bbc2cb4e87d633a09a2a55c00c319f4ec34ed991ac0067486451449f3c28d07b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f3e14c973cc0002441de809d6e219aafb0fc84a1cedbdf214ef4aa44c46ace6",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-05-04T00:20:06Z",
    "title_canon_sha256": "aeb5eac79ad73d8bf69b35f45c1d2383458b05c862fd9d3688f66c0513796e07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1005.0424",
    "kind": "arxiv",
    "version": 1
  }
}