Pith Number

pith:RQPFH5IB

pith:2025:RQPFH5IBEP5APHZWL2CI5PO7RT

not attested not anchored not stored refs pending

Lectures on bar and cobar

Fritz H\"ormann

arxiv:2507.15133 v1 · 2025-07-20 · 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{RQPFH5IBEP5APHZWL2CI5PO7RT}

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	2026-07-05T11:40:18.921347Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c1e53f50123fa079f365e848ebddf8cdf4fe3fe68125e5422de1491760a0c37

Aliases

arxiv: 2507.15133 · arxiv_version: 2507.15133v1 · doi: 10.48550/arxiv.2507.15133 · pith_short_12: RQPFH5IBEP5A · pith_short_16: RQPFH5IBEP5APHZW · pith_short_8: RQPFH5IB

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/RQPFH5IBEP5APHZWL2CI5PO7RT \
  | 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: 8c1e53f50123fa079f365e848ebddf8cdf4fe3fe68125e5422de1491760a0c37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c753900c3ebd52363be7671023d0cdbe63760e6d32e8ba0f97fa5400a9cefede",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2025-07-20T21:49:31Z",
    "title_canon_sha256": "1befc38d7ebb553b9ccb161523414528f4c0daa74e4176696bad3620b73fec65"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15133",
    "kind": "arxiv",
    "version": 1
  }
}