Pith Number

pith:N72UD2IX

pith:2021:N72UD2IX52EMCOANLDFRSOQHJC

not attested not anchored not stored refs pending

Categorical blow-up formula for Hilbert schemes of points

Naoki Koseki

arxiv:2110.08315 v4 · 2021-10-15 · 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{N72UD2IX52EMCOANLDFRSOQHJC}

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	2026-07-05T06:37:47.635390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ff541e917ee88c1380d58cb193a07488eaf3434fe642c87db2a451036e11e70

Aliases

arxiv: 2110.08315 · arxiv_version: 2110.08315v4 · doi: 10.48550/arxiv.2110.08315 · pith_short_12: N72UD2IX52EM · pith_short_16: N72UD2IX52EMCOAN · pith_short_8: N72UD2IX

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/N72UD2IX52EMCOANLDFRSOQHJC \
  | 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: 6ff541e917ee88c1380d58cb193a07488eaf3434fe642c87db2a451036e11e70

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9e37c4c0062c8accafe9fdb85f01ce93437e92a2ccd1929cc52b1f5b472da6fd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2021-10-15T18:49:28Z",
    "title_canon_sha256": "32a1c1e8282ea2951b10382d985cef74f5343aed75c1b7ce784191e87645b4e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2110.08315",
    "kind": "arxiv",
    "version": 4
  }
}