Pith Number

pith:BVABWMV3

pith:2011:BVABWMV3AJZXVEEZE7D5Y4AE55

not attested not anchored not stored refs pending

Two papers which changed my life: Milnor's seminal work on flat manifolds and flat bundles

William M. Goldman

arxiv:1108.0216 v2 · 2011-08-01 · math.DG · 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{BVABWMV3AJZXVEEZE7D5Y4AE55}

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	2026-05-18T03:58:24.652903Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d401b32bb02737a909927c7dc7004ef5e9838495dba613fd6537baa7fe60ab4

Aliases

arxiv: 1108.0216 · arxiv_version: 1108.0216v2 · doi: 10.48550/arxiv.1108.0216 · pith_short_12: BVABWMV3AJZX · pith_short_16: BVABWMV3AJZXVEEZ · pith_short_8: BVABWMV3

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/BVABWMV3AJZXVEEZE7D5Y4AE55 \
  | 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: 0d401b32bb02737a909927c7dc7004ef5e9838495dba613fd6537baa7fe60ab4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4801e8b0f9d14ce442f461d709446c0ebd9dba17a22985af494e8d61bb20d21d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-08-01T01:16:18Z",
    "title_canon_sha256": "09b13c8983ebdc1a0f320a79170a2353641ac3d3326b441bed8feae6ecedac4d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.0216",
    "kind": "arxiv",
    "version": 2
  }
}