Pith Number

pith:TNDQDQSS

pith:2026:TNDQDQSSSENQX4JS3IVVHXCYVY

not attested not anchored not stored refs pending

Directed univalence for simplicial objects in an $\infty$-topos

Christian Sattler, Emily Riehl, Evan Cavallo

arxiv:2607.02420 v1 · 2026-07-02 · math.CT · 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{TNDQDQSSSENQX4JS3IVVHXCYVY}

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	2026-07-03T01:17:58.756289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b4701c252911b0bf132da2b53dc58ae2c68036c44b41a1c340078b15511060e

Aliases

arxiv: 2607.02420 · arxiv_version: 2607.02420v1 · doi: 10.48550/arxiv.2607.02420 · pith_short_12: TNDQDQSSSENQ · pith_short_16: TNDQDQSSSENQX4JS · pith_short_8: TNDQDQSS

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/TNDQDQSSSENQX4JS3IVVHXCYVY \
  | 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: 9b4701c252911b0bf132da2b53dc58ae2c68036c44b41a1c340078b15511060e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c41000b47c54906395179bf69ca8d5a74ccad44063df7710a93b1f35709e628",
    "cross_cats_sorted": [
      "math.AT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2026-07-02T16:50:07Z",
    "title_canon_sha256": "1f34e2f1744d368557e35d4193d6447953bb5d424849f4d9886effefabc4e435"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.02420",
    "kind": "arxiv",
    "version": 1
  }
}