Pith Number

pith:4EN7BLZA

pith:2016:4EN7BLZAP7ZAEL7RKEPCAIIDLN

not attested not anchored not stored refs pending

On Geometric Analysis of the Dynamics of Volumetric Expansion

Sergey Stepanov

arxiv:1612.08853 v1 · 2016-12-28 · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4EN7BLZAP7ZAEL7RKEPCAIIDLN}

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	2026-05-18T00:53:47.006416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e11bf0af207ff2022ff1511e2021035b79bb5f9a1500c4d588d91acc1ce6f15c

Aliases

arxiv: 1612.08853 · arxiv_version: 1612.08853v1 · doi: 10.48550/arxiv.1612.08853 · pith_short_12: 4EN7BLZAP7ZA · pith_short_16: 4EN7BLZAP7ZAEL7R · pith_short_8: 4EN7BLZA

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/4EN7BLZAP7ZAEL7RKEPCAIIDLN \
  | 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: e11bf0af207ff2022ff1511e2021035b79bb5f9a1500c4d588d91acc1ce6f15c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "248170cd23e9176abd33407084240c9e814e721ee3b5e1ea85b02d16a8cc9a61",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2016-12-28T11:15:21Z",
    "title_canon_sha256": "b3cab980654ae66bed097c14c947a0016117dce6023313a16aad2947d75dfec8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.08853",
    "kind": "arxiv",
    "version": 1
  }
}