Pith Number

pith:AKTCSJUT

pith:2010:AKTCSJUTE5SZ6SB5P6353443XW

not attested not anchored not stored refs pending

Construction of schemes over $F_1$, and over idempotent semirings: towards tropical geometry

Satoshi Takagi

arxiv:1009.0121 v6 · 2010-09-01 · 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{AKTCSJUTE5SZ6SB5P6353443XW}

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	2026-05-18T04:21:00.585307Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02a629269327659f483d7fb7ddf39bbd8c1be2f1ad5e25bd5075b5cdd82ed986

Aliases

arxiv: 1009.0121 · arxiv_version: 1009.0121v6 · doi: 10.48550/arxiv.1009.0121 · pith_short_12: AKTCSJUTE5SZ · pith_short_16: AKTCSJUTE5SZ6SB5 · pith_short_8: AKTCSJUT

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/AKTCSJUTE5SZ6SB5P6353443XW \
  | 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: 02a629269327659f483d7fb7ddf39bbd8c1be2f1ad5e25bd5075b5cdd82ed986

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fd4cbf74538b626870a9339ef0df8415c5080e99ba7a45c76f9d63e2622669fb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2010-09-01T09:04:05Z",
    "title_canon_sha256": "5e6a0e34025ac5b0e770885f97cadc984807530aedea9ab385388d2449e0f620"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.0121",
    "kind": "arxiv",
    "version": 6
  }
}