Pith Number

pith:X6YLL6KJ

pith:2013:X6YLL6KJGHXFSOJFBPEEUSLEAT

not attested not anchored not stored refs pending

On topological complexity of twisted products

Alexander Dranishnikov

arxiv:1312.0170 v1 · 2013-12-01 · math.GT · math.AT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6YLL6KJGHXFSOJFBPEEUSLEAT}

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	2026-05-18T03:05:46.540404Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfb0b5f94931ee5939250bc84a496404d538f0c9ed6369e11a5259c2ab41569d

Aliases

arxiv: 1312.0170 · arxiv_version: 1312.0170v1 · doi: 10.48550/arxiv.1312.0170 · pith_short_12: X6YLL6KJGHXF · pith_short_16: X6YLL6KJGHXFSOJF · pith_short_8: X6YLL6KJ

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/X6YLL6KJGHXFSOJFBPEEUSLEAT \
  | 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: bfb0b5f94931ee5939250bc84a496404d538f0c9ed6369e11a5259c2ab41569d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "585688cba514681ea6cbcb8e3adf1439c8ecc7fb2df24db0cdaf07e1359b5b25",
    "cross_cats_sorted": [
      "math.AT",
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2013-12-01T01:35:54Z",
    "title_canon_sha256": "d1d834243ee5c990ef2f35d5d167d50c39f014975c118e89ebf32ae33835bfb6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.0170",
    "kind": "arxiv",
    "version": 1
  }
}