Pith Number

pith:GB7RTH6U

pith:2016:GB7RTH6UBCVLJVFXWUY22TJ6EW

not attested not anchored not stored refs pending

Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over $\mathbb{F}_q[[t]]$

Yigeng Zhao

arxiv:1611.08722 v2 · 2016-11-26 · math.AG · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GB7RTH6UBCVLJVFXWUY22TJ6EW}

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	2026-05-17T23:57:15.909446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

307f199fd408aab4d4b7b531ad4d3e2594209a4caa341878036d4832b2fae172

Aliases

arxiv: 1611.08722 · arxiv_version: 1611.08722v2 · doi: 10.48550/arxiv.1611.08722 · pith_short_12: GB7RTH6UBCVL · pith_short_16: GB7RTH6UBCVLJVFX · pith_short_8: GB7RTH6U

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/GB7RTH6UBCVLJVFXWUY22TJ6EW \
  | 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: 307f199fd408aab4d4b7b531ad4d3e2594209a4caa341878036d4832b2fae172

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a30e6bfe56b7eabd62ccf35565304c709c39d03ccf3f13c92e982bc934278e37",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-11-26T17:06:13Z",
    "title_canon_sha256": "5febb74a0b395b825c876d929d8220e0139af798c21905919ba035089b889e2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.08722",
    "kind": "arxiv",
    "version": 2
  }
}