Pith Number

pith:LSMCEKBT

pith:2019:LSMCEKBTG7TFAU5MC5CKUNUPU3

not attested not anchored not stored refs pending

On the stabilization of the Betti numbers of the moduli space of sheaves on $\mathbb{P}^2$

Sayanta Mandal

arxiv:1908.09977 v2 · 2019-08-27 · 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{LSMCEKBTG7TFAU5MC5CKUNUPU3}

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	2026-07-05T00:51:30.310227Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5c9822283337e65053ac1744aa368fa6d9d0c5baf9008855cde738b71e3e1943

Aliases

arxiv: 1908.09977 · arxiv_version: 1908.09977v2 · doi: 10.48550/arxiv.1908.09977 · pith_short_12: LSMCEKBTG7TF · pith_short_16: LSMCEKBTG7TFAU5M · pith_short_8: LSMCEKBT

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/LSMCEKBTG7TFAU5MC5CKUNUPU3 \
  | 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: 5c9822283337e65053ac1744aa368fa6d9d0c5baf9008855cde738b71e3e1943

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b1051661ea41330058b17b32f64b81244c63a302866837b58b3479aebb0cc8f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2019-08-27T01:30:06Z",
    "title_canon_sha256": "d2b9ca6fd7760204cf2e372bf9be750b02363b58a6b59b7a999b01d95c0474a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.09977",
    "kind": "arxiv",
    "version": 2
  }
}