Pith Number

pith:MUJ6AYHG

pith:2015:MUJ6AYHGHI4LUWJVXBZVKO2O7T

not attested not anchored not stored refs pending

Lower bounds on projective levels of complexes

Elo\'isa Grifo, Hannah Altmann, Jonathan Monta\~no, Thanh Vu, William Sanders

arxiv:1512.08534 v2 · 2015-12-28 · 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{MUJ6AYHGHI4LUWJVXBZVKO2O7T}

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	2026-05-18T00:33:44.241695Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6513e060e63a38ba5935b873553b4efcf040e11453d695358f60983e327ca9c9

Aliases

arxiv: 1512.08534 · arxiv_version: 1512.08534v2 · doi: 10.48550/arxiv.1512.08534 · pith_short_12: MUJ6AYHGHI4L · pith_short_16: MUJ6AYHGHI4LUWJV · pith_short_8: MUJ6AYHG

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/MUJ6AYHGHI4LUWJVXBZVKO2O7T \
  | 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: 6513e060e63a38ba5935b873553b4efcf040e11453d695358f60983e327ca9c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "17f526e7f97007dbe352a599c42c4279612ca11e86f8d9f7a884e0e8104a53c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-12-28T21:25:30Z",
    "title_canon_sha256": "4894f2ca84526692bdb3c6e8e59a601a5603a44d0a68dc8a38705fb26b98a759"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.08534",
    "kind": "arxiv",
    "version": 2
  }
}