Pith Number

pith:K4UCAQ76

pith:2019:K4UCAQ76CHUV2X3BDVREXIMOYU

not attested not anchored not stored refs pending

All $(\infty,1)$-toposes have strict univalent universes

Michael Shulman

arxiv:1904.07004 v2 · 2019-04-15 · 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{K4UCAQ76CHUV2X3BDVREXIMOYU}

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.

Cited by

5 papers in Pith

Constructive higher sheaf models with applications to synthetic mathematics

From Copying to Corelations via Ancestry Partitions

Elementary $\infty$-toposes from type theory

Constructive higher sheaf models with applications to synthetic mathematics

Univalence without function extensionality

Receipt and verification

First computed	2026-05-17T23:47:39.209918Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57282043fe11e95d5f611d624ba18ec536f3e9344a014b77cae02362c09d4649

Aliases

arxiv: 1904.07004 · arxiv_version: 1904.07004v2 · doi: 10.48550/arxiv.1904.07004 · pith_short_12: K4UCAQ76CHUV · pith_short_16: K4UCAQ76CHUV2X3B · pith_short_8: K4UCAQ76

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/K4UCAQ76CHUV2X3BDVREXIMOYU \
  | 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: 57282043fe11e95d5f611d624ba18ec536f3e9344a014b77cae02362c09d4649

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8d0594cb8fe8d0044c42bd0b2c31673ca02eba873c0e621afe454da1434828c",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2019-04-15T12:45:00Z",
    "title_canon_sha256": "8620ee5a275de66a4de4cbbb729b4d07a6db4694b3de23b32070d56555e4e283"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.07004",
    "kind": "arxiv",
    "version": 2
  }
}