Pith Number

pith:YKVAR4XD

pith:2016:YKVAR4XDUJQO6RZLWHVOPNH5TE

not attested not anchored not stored refs pending

Very flat, locally very flat, and contraadjusted modules

Alexander Slavik, Jan Trlifaj

arxiv:1601.00783 v2 · 2016-01-05 · 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{YKVAR4XDUJQO6RZLWHVOPNH5TE}

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.

Cited by

1 paper in Pith

Contraherent cosheaves of contramodules on Noetherian formal schemes

Receipt and verification

First computed	2026-05-17T23:56:56.283374Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2aa08f2e3a260ef472bb1eae7b4fd991df0b1648a8ba317fccdaf37aae971f4

Aliases

arxiv: 1601.00783 · arxiv_version: 1601.00783v2 · doi: 10.48550/arxiv.1601.00783 · pith_short_12: YKVAR4XDUJQO · pith_short_16: YKVAR4XDUJQO6RZL · pith_short_8: YKVAR4XD

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/YKVAR4XDUJQO6RZLWHVOPNH5TE \
  | 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: c2aa08f2e3a260ef472bb1eae7b4fd991df0b1648a8ba317fccdaf37aae971f4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b1766bc3ab6bf914664d934b2415f5324de8df1d6fbf47a39a02629edd0a94eb",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2016-01-05T10:28:04Z",
    "title_canon_sha256": "ed8fa42fefee4c8b29a245bb8131688d47d306a47732c8eb06f91f2f769fe534"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1601.00783",
    "kind": "arxiv",
    "version": 2
  }
}