Pith Number

pith:FNUSJSIL

pith:2026:FNUSJSILWJX2GVWUA2ZGV63A23

not attested not anchored not stored refs pending

Structured Quotients in Real Homotopy Theory

Qi Zhu, Ryan Quinn

arxiv:2606.25898 v1 · 2026-06-24 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FNUSJSILWJX2GVWUA2ZGV63A23}

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	2026-06-25T01:18:42.652062Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b6924c90bb26fa356d406b26afb60d6d3bfc90c7f89d0c5d936acc71a4272d2

Aliases

arxiv: 2606.25898 · arxiv_version: 2606.25898v1 · doi: 10.48550/arxiv.2606.25898 · pith_short_12: FNUSJSILWJX2 · pith_short_16: FNUSJSILWJX2GVWU · pith_short_8: FNUSJSIL

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/FNUSJSILWJX2GVWUA2ZGV63A23 \
  | 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: 2b6924c90bb26fa356d406b26afb60d6d3bfc90c7f89d0c5d936acc71a4272d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8909ce0fd52f69e8a021a2e5c774720857b5c5be7ae896feab4f50912195ef07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-06-24T14:46:57Z",
    "title_canon_sha256": "1bb89dafecc5b20406c168ff64d94b6b756b878452c4802ed3208d7398c8ab7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.25898",
    "kind": "arxiv",
    "version": 1
  }
}