Pith Number

pith:IKVBQM5G

pith:2025:IKVBQM5GYJXHB4SCX2U3RIFZHV

not attested not anchored not stored refs pending

The nonexistence of sections of Stiefel varieties and stably free modules

Sebastian Gant

arxiv:2509.07263 v3 · 2025-09-08 · math.AG · math.AC · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IKVBQM5GYJXHB4SCX2U3RIFZHV}

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	2026-05-20T00:00:23.851788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

42aa1833a6c26e70f242bea9b8a0b93d752ea7eb51228d7bbd9452f616887626

Aliases

arxiv: 2509.07263 · arxiv_version: 2509.07263v3 · doi: 10.48550/arxiv.2509.07263 · pith_short_12: IKVBQM5GYJXH · pith_short_16: IKVBQM5GYJXHB4SC · pith_short_8: IKVBQM5G

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/IKVBQM5GYJXHB4SCX2U3RIFZHV \
  | 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: 42aa1833a6c26e70f242bea9b8a0b93d752ea7eb51228d7bbd9452f616887626

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "73f386693d15e836a1bf9416e15a55d8cbb3b08de18dfaa3cd3911b5d24c9ea4",
    "cross_cats_sorted": [
      "math.AC",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-09-08T22:43:58Z",
    "title_canon_sha256": "86fe7a24081f224022121d9bce9ffddd826d9f2331ebe38c9d2db9d8d57b1306"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07263",
    "kind": "arxiv",
    "version": 3
  }
}