Pith Number

pith:FGI2LTX5

pith:2011:FGI2LTX5ZIZYRIZTZFLGCJJ2JM

not attested not anchored not stored refs pending

Homotopy coherent diagrams and approximate fibrations

Wolfgang Steimle

arxiv:1107.5213 v3 · 2011-07-26 · math.AT · 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{FGI2LTX5ZIZYRIZTZFLGCJJ2JM}

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	2026-05-18T04:12:10.116918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2991a5cefdca3388a333c95661253a4b268aaf221baae43c10dd3892623b82a2

Aliases

arxiv: 1107.5213 · arxiv_version: 1107.5213v3 · doi: 10.48550/arxiv.1107.5213 · pith_short_12: FGI2LTX5ZIZY · pith_short_16: FGI2LTX5ZIZYRIZT · pith_short_8: FGI2LTX5

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/FGI2LTX5ZIZYRIZTZFLGCJJ2JM \
  | 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: 2991a5cefdca3388a333c95661253a4b268aaf221baae43c10dd3892623b82a2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff5e6f97572987a6ca3f4d74e4433d7293d4b36fc64eccb888a9171b7435d220",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-07-26T13:45:33Z",
    "title_canon_sha256": "3e2d7515eb6c9d58eee125c35e06da3d5075a0ec93da9cd27ec77b9e46c3c025"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.5213",
    "kind": "arxiv",
    "version": 3
  }
}