Pith Number

pith:6VU2N2Y4

pith:2008:6VU2N2Y427PQ72IOZWRSIRKTZX

not attested not anchored not stored refs pending

Algebraic colimit calculations in homotopy theory using fibred and cofibred categories

Rafael Sivera, Ronald Brown

arxiv:0809.4192 v2 · 2008-09-24 · math.AT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6VU2N2Y427PQ72IOZWRSIRKTZX}

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	2026-05-18T03:10:37.876720Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f569a6eb1cd7df0fe90ecda3244553cdd677c706e662f146ccfc427a3c28277f

Aliases

arxiv: 0809.4192 · arxiv_version: 0809.4192v2 · doi: 10.48550/arxiv.0809.4192 · pith_short_12: 6VU2N2Y427PQ · pith_short_16: 6VU2N2Y427PQ72IO · pith_short_8: 6VU2N2Y4

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/6VU2N2Y427PQ72IOZWRSIRKTZX \
  | 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: f569a6eb1cd7df0fe90ecda3244553cdd677c706e662f146ccfc427a3c28277f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a58ffa4a73918a3de60ce6b14d152d6bc09b71acbdc92fcc7aabdc7d3c57b14",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2008-09-24T14:02:34Z",
    "title_canon_sha256": "998eed331d09f6bb05009c24154eabc556ff5524da4cb0bfc4a29b16f019c816"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0809.4192",
    "kind": "arxiv",
    "version": 2
  }
}