Pith Number

pith:5PZFBGUC

pith:2019:5PZFBGUCTNK62IEQZW45Q2DI6N

not attested not anchored not stored refs pending

Iterated traces in 2-categories and Lefschetz theorems

Jonathan A. Campbell, Kate Ponto

arxiv:1908.07497 v2 · 2019-08-20 · 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{5PZFBGUCTNK62IEQZW45Q2DI6N}

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	2026-07-05T04:47:05.876852Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebf2509a829b55ed2090cdb9d86868f357e8853f8b285a1bacd6280e4bf0cb2d

Aliases

arxiv: 1908.07497 · arxiv_version: 1908.07497v2 · doi: 10.48550/arxiv.1908.07497 · pith_short_12: 5PZFBGUCTNK6 · pith_short_16: 5PZFBGUCTNK62IEQ · pith_short_8: 5PZFBGUC

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/5PZFBGUCTNK62IEQZW45Q2DI6N \
  | 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: ebf2509a829b55ed2090cdb9d86868f357e8853f8b285a1bacd6280e4bf0cb2d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "499f1725bce6ed576a83dfc1db9ee8a9c28dc44febc2e05b9b8a688546cb8859",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2019-08-20T17:19:25Z",
    "title_canon_sha256": "5d9f77522bc786bc4df1dba3ae4c05e15272bbd98f44aed41d07f0bb9dd4d79b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.07497",
    "kind": "arxiv",
    "version": 2
  }
}