Pith Number

pith:QPPEX6R7

pith:2015:QPPEX6R7TX6IQQRBED5V6IE5JB

not attested not anchored not stored refs pending

Witt, $GW$, $K$-theory of quasi-projective schemes

Satya Mandal

arxiv:1507.03978 v3 · 2015-07-14 · math.AC · math.AG · 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{QPPEX6R7TX6IQQRBED5V6IE5JB}

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	2026-05-18T01:33:34.873676Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83de4bfa3f9dfc88422120fb5f209d4879e33e8b68022cf62c836e2ec5723e10

Aliases

arxiv: 1507.03978 · arxiv_version: 1507.03978v3 · doi: 10.48550/arxiv.1507.03978 · pith_short_12: QPPEX6R7TX6I · pith_short_16: QPPEX6R7TX6IQQRB · pith_short_8: QPPEX6R7

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/QPPEX6R7TX6IQQRBED5V6IE5JB \
  | 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: 83de4bfa3f9dfc88422120fb5f209d4879e33e8b68022cf62c836e2ec5723e10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fad54dc95240528a29e5d2504e48b2ecfc840beadc4618c23b1d42bffb0ef7f9",
    "cross_cats_sorted": [
      "math.AG",
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-07-14T19:40:48Z",
    "title_canon_sha256": "fa294b3df7a5e21be24f764c08b5451f9d7cfb154035ba2f5e36f7134233fdcf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.03978",
    "kind": "arxiv",
    "version": 3
  }
}