Pith Number

pith:CB53SJB2

pith:1998:CB53SJB2KY4GZI2XGRNSMT2QCO

not attested not anchored not stored refs pending

Algebraic Shifting Increases Relative Homology

Art M. Duval

arxiv:math/9809195 v1 · 1998-09-30 · math.AT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CB53SJB2KY4GZI2XGRNSMT2QCO}

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	2026-05-18T01:05:33.728902Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

107bb9243a56386ca357345b264f5013880985356fb91789de1cdf54b78e6248

Aliases

arxiv: math/9809195 · arxiv_version: math/9809195v1 · doi: 10.48550/arxiv.math/9809195 · pith_short_12: CB53SJB2KY4G · pith_short_16: CB53SJB2KY4GZI2X · pith_short_8: CB53SJB2

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/CB53SJB2KY4GZI2XGRNSMT2QCO \
  | 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: 107bb9243a56386ca357345b264f5013880985356fb91789de1cdf54b78e6248

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4c77768b355e07af46bdc98a418f887089c0280b60bdc1c0c19aae742499fdc",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.AT",
    "submitted_at": "1998-09-30T20:09:09Z",
    "title_canon_sha256": "944aa2fe1a47c1ef237d5fd6b4d6eb59e1a6dfcde266f8ef38fe3cc79aaabd3b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9809195",
    "kind": "arxiv",
    "version": 1
  }
}