Pith Number

pith:D6KNCE3B

pith:2006:D6KNCE3BE76CDDXH27DZJ5X5D6

not attested not anchored not stored refs pending

Homotopy limits and colimits and enriched homotopy theory

Michael Shulman

arxiv:math/0610194 v3 · 2006-10-05 · 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{D6KNCE3BE76CDDXH27DZJ5X5D6}

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	2026-07-04T15:45:20.237697Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f94d1136127fc218ee7d7c794f6fd1f8f6db6106a6bbddefbcbe1b04c223a8b

Aliases

arxiv: math/0610194 · arxiv_version: math/0610194v3 · doi: 10.48550/arxiv.math/0610194 · pith_short_12: D6KNCE3BE76C · pith_short_16: D6KNCE3BE76CDDXH · pith_short_8: D6KNCE3B

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/D6KNCE3BE76CDDXH27DZJ5X5D6 \
  | 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: 1f94d1136127fc218ee7d7c794f6fd1f8f6db6106a6bbddefbcbe1b04c223a8b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fcf2b71ebae8cae6623f8591591bfea8fcd031c72564550141df913bfc04f537",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2006-10-05T14:48:41Z",
    "title_canon_sha256": "b93018874d3e9d338c07bac06c9d5f7259e52da5240d580fc9207223b0f8b811"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610194",
    "kind": "arxiv",
    "version": 3
  }
}