Pith Number

pith:GGZVMUBA

pith:2023:GGZVMUBAWYWGNSDPKJ6MWUUIBJ

not attested not anchored not stored refs pending

Ng\^o support theorem and polarizability of quasi-projective commutative group schemes

Dragos Fratila, Giuseppe Ancona

arxiv:2304.07729 v3 · 2023-04-16 · 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{GGZVMUBAWYWGNSDPKJ6MWUUIBJ}

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	2026-05-20T14:03:16.483220Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31b3565020b62c66c86f527ccb52880a6607898c7867eef241a8305649a8f042

Aliases

arxiv: 2304.07729 · arxiv_version: 2304.07729v3 · doi: 10.48550/arxiv.2304.07729 · pith_short_12: GGZVMUBAWYWG · pith_short_16: GGZVMUBAWYWGNSDP · pith_short_8: GGZVMUBA

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/GGZVMUBAWYWGNSDPKJ6MWUUIBJ \
  | 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: 31b3565020b62c66c86f527ccb52880a6607898c7867eef241a8305649a8f042

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "aecb3bd8c3feed9daa058bb27ec07e027e06aa0913361d3a53c8b26aebef4de9",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2023-04-16T08:54:50Z",
    "title_canon_sha256": "b717b1482b22a6dd07ebb0227b8bde3ee2989b2992c77965751aaa3a4f74528d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2304.07729",
    "kind": "arxiv",
    "version": 3
  }
}