Pith Number

pith:ZCPJKZZK

pith:2019:ZCPJKZZKPRN45FBQD7WUZIA7YE

not attested not anchored not stored refs pending

$n$-excisive functors, canonical connections, and line bundles on the Ran space

James Tao

arxiv:1906.07976 v1 · 2019-06-19 · math.AG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZCPJKZZKPRN45FBQD7WUZIA7YE}

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	2026-05-17T23:42:54.996819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c89e95672a7c5bce94301fed4ca01fc126d1f8aee1cd2a284ef57192d448814d

Aliases

arxiv: 1906.07976 · arxiv_version: 1906.07976v1 · doi: 10.48550/arxiv.1906.07976 · pith_short_12: ZCPJKZZKPRN4 · pith_short_16: ZCPJKZZKPRN45FBQ · pith_short_8: ZCPJKZZK

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/ZCPJKZZKPRN45FBQD7WUZIA7YE \
  | 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: c89e95672a7c5bce94301fed4ca01fc126d1f8aee1cd2a284ef57192d448814d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ae7d543416cda57702cfbfddeb893c331bcc0a62aaaf04c9f80853b5228dc0e",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-06-19T08:52:58Z",
    "title_canon_sha256": "afb9997f98ca58c294faa909f8522cde0ebcc3c35081bf0f0396dfb99b32fac2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.07976",
    "kind": "arxiv",
    "version": 1
  }
}