Pith Number

pith:L7SEMNKF

pith:2026:L7SEMNKFB3HPC35ASNK3O7QLTD

not attested not anchored not stored refs pending

Removing the Torsion-free Hypothesis in a Positivity Theorem on Deligne-Mumford Stacks

Jihao Liu, Shengyu Hou

arxiv:2607.26989 v1 · 2026-07-29 · 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{L7SEMNKFB3HPC35ASNK3O7QLTD}

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	2026-07-30T01:23:15.859568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

5fe44635450ecef16fa09355b77e0b98d3f1719b3537b1c1059f58b8ecaf0428

Aliases

arxiv: 2607.26989 · arxiv_version: 2607.26989v1 · doi: 10.48550/arxiv.2607.26989 · pith_short_12: L7SEMNKFB3HP · pith_short_16: L7SEMNKFB3HPC35A · pith_short_8: L7SEMNKF

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/L7SEMNKFB3HPC35ASNK3O7QLTD \
  | 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: 5fe44635450ecef16fa09355b77e0b98d3f1719b3537b1c1059f58b8ecaf0428

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "49a6b8acab70041f3dc50ee7136f90ef724e64d603541d76c48f8e92269c1378",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-07-29T14:47:46Z",
    "title_canon_sha256": "d16108f6bd65c7d53b5a279547e6829d9358fec2af9a65216a9b43f011e596ee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26989",
    "kind": "arxiv",
    "version": 1
  }
}