Pith Number

pith:R4XQJNHE

pith:2016:R4XQJNHE42DYXMVO4OZUKXIFWK

not attested not anchored not stored refs pending

Geometric characterization of flat modules

Carlos Sancho, Fernando Sancho, Pedro Sancho

arxiv:1609.08327 v5 · 2016-09-27 · math.AG · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R4XQJNHE42DYXMVO4OZUKXIFWK}

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	2026-05-18T00:33:07.073108Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8f2f04b4e4e6878bb2aee3b3455d05b2836073bab64c783821dae2a23bfdcf03

Aliases

arxiv: 1609.08327 · arxiv_version: 1609.08327v5 · doi: 10.48550/arxiv.1609.08327 · pith_short_12: R4XQJNHE42DY · pith_short_16: R4XQJNHE42DYXMVO · pith_short_8: R4XQJNHE

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/R4XQJNHE42DYXMVO4OZUKXIFWK \
  | 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: 8f2f04b4e4e6878bb2aee3b3455d05b2836073bab64c783821dae2a23bfdcf03

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3d01d20dd3566a90841c2aa901abc306ce7b1d29f5f0985bacfa94e5bfa39b9b",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2016-09-27T09:24:27Z",
    "title_canon_sha256": "a16be4fd56f487c7fec1e6ba772c0bdeec412e4ef1c0d1d8bebff37e53a72687"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1609.08327",
    "kind": "arxiv",
    "version": 5
  }
}