diff --git a/tests/test_deserialize.py b/tests/test_deserialize.py
index 33b1a4e..ccb9191 100644
--- a/tests/test_deserialize.py
+++ b/tests/test_deserialize.py
@@ -601,6 +601,18 @@ def test_round_trip_keeps_the_facts(model: XbrlModel, fmt: str) -> None:
   assert cash.unit_id == next(u.id for u in got.units if u.measure == "iso4217:USD")
 
 
+def test_tavi_reads_an_exact_fact_as_infinitely_precise(model: XbrlModel) -> None:
+  """TAVI writes INF by leaving `decimals` out; the reader must not read that
+  as unknown, or an exact fact loses to a rounded duplicate of itself."""
+  assets = next(f for f in model.facts if f.concept_qname == "us-gaap:Assets")
+  assets.decimals = "INF"
+  got = from_tavi_json(to_tavi(model))
+  back = next(f for f in got.facts if f.concept_qname == "us-gaap:Assets")
+  assert back.decimals == "INF"
+  text = next(f for f in got.facts if f.concept_qname == "dei:DocumentType")
+  assert text.decimals is None
+
+
 @pytest.mark.parametrize("fmt", ["tavi", "holon"])
 def test_round_trip_keeps_the_networks(model: XbrlModel, fmt: str) -> None:
   got = _through(model, fmt)
diff --git a/tests/test_published.py b/tests/test_published.py
index 3460bc9..d022c76 100644
--- a/tests/test_published.py
+++ b/tests/test_published.py
@@ -24,7 +24,7 @@
 from tests.test_deserialize import _model
 from xbrlkit.config import Config
 from xbrlkit.model import Concept, Label, XbrlFact, XbrlModel
-from xbrlkit.serialize import to_holon
+from xbrlkit.serialize import to_holon, to_tavi
 from xbrlkit.serve import tools
 from xbrlkit.serve.session import FilingSession, PublishedFiling
 
@@ -341,7 +341,7 @@ def test_a_missing_fragment_stays_a_url_and_the_load_succeeds(
 
 
 @pytest.mark.unit
-def test_a_manifest_without_a_holon_is_not_a_published_filing() -> None:
+def test_a_manifest_without_a_model_is_not_a_published_filing() -> None:
   from xbrlkit.serve.session import _published_from
 
   assert (
@@ -354,6 +354,68 @@ def test_a_manifest_without_a_holon_is_not_a_published_filing() -> None:
   assert published == PublishedFiling(
     accession="acc", holon_url="http://x/f/holon.jsonld"
   )
+  # A filing published as a TAVI model alone is still a published filing.
+  only_tavi = _published_from(
+    "acc", [{"kind": "tavi", "name": "tavi.json"}], "http://x/f/"
+  )
+  assert only_tavi == PublishedFiling(accession="acc", tavi_url="http://x/f/tavi.json")
+  assert only_tavi.model_urls == ["http://x/f/tavi.json"]
+
+
+def _publish_tavi(tmp_path: Path, base: str, *, reachable: bool = True) -> None:
+  """List a TAVI model in the ACME catalog ahead of the holon; write the file
+  only when it should be reachable. The TAVI carries its text block inline."""
+  folder = f"{base}/2024/{CIK}/{ACCESSION}"
+  root = tmp_path / "2024" / CIK / ACCESSION
+  if reachable:
+    model = _model_with_text()
+    for fact in model.facts:
+      if fact.value_str == "__FRAGMENT_URL__":
+        fact.value_str = FRAGMENT
+    (root / "tavi.json").write_text(to_tavi(model))
+  catalog_path = tmp_path / "companies" / "acme.json"
+  catalog = json.loads(catalog_path.read_text())
+  newest = catalog["filings"][0]
+  newest["representations"] = [
+    {"kind": "tavi", "name": "tavi.json", "url": f"{folder}/tavi.json"},
+    *newest["representations"],
+  ]
+  catalog_path.write_text(json.dumps(catalog))
+
+
+@pytest.mark.unit
+def test_a_ticker_loads_the_published_tavi_first(
+  cdn: str, tmp_path: Path, no_edgar
+) -> None:
+  _publish_tavi(tmp_path, cdn)
+  session = _session(cdn)
+  try:
+    loaded = session.load("ACME")
+    assert loaded.source_kind == "tavi"
+    assert loaded.has_document is True
+    assert tools.fact_grid(loaded, ["us-gaap:Assets"])["rows"][0]["value"] == 1000.0
+    block = next(
+      f
+      for f in loaded.model.facts
+      if f.concept_qname == "us-gaap:LesseeOperatingLeasesTextBlock"
+    )
+    assert block.value_str == FRAGMENT
+  finally:
+    session.close()
+
+
+@pytest.mark.unit
+def test_an_unreachable_tavi_falls_back_to_the_holon(
+  cdn: str, tmp_path: Path, no_edgar
+) -> None:
+  _publish_tavi(tmp_path, cdn, reachable=False)
+  session = _session(cdn)
+  try:
+    loaded = session.load("ACME")
+    assert loaded.source_kind == "holon"
+    assert tools.fact_grid(loaded, ["us-gaap:Assets"])["rows"][0]["value"] == 1000.0
+  finally:
+    session.close()
 
 
 # ── The filer's identity ───────────────────────────────────────────────────
diff --git a/xbrlkit/deserialize/tavi.py b/xbrlkit/deserialize/tavi.py
index 895a288..9d842e6 100644
--- a/xbrlkit/deserialize/tavi.py
+++ b/xbrlkit/deserialize/tavi.py
@@ -22,9 +22,9 @@
 - the derived period semantics (duration bucket, calendar placement) — the one
   exception, recomputed by :mod:`xbrlkit.periods` from the dates themselves,
   which is where the parse gets them too;
-- the abstractness of axes, domains and members: the emitter turns those
-  elements into dimensional objects, and TAVI has no flag for it (a hypercube
-  is marked ``is_hypercube_item`` when its role presents the table);
+- nothing further on the dimensional elements: axes, domains and members are
+  objects of their own in TAVI, so they read back abstract, and a hypercube is
+  marked ``is_hypercube_item`` when its role presents the table;
 - reference linkbase entries, ``Network.role_id``, a fact's source hash and
   raw lexical value, and a dimension's segment/scenario axis;
 - a fact's own entity when it differs from the report's — the emitter writes
@@ -200,7 +200,6 @@ def _read(document: Mapping[str, Any]) -> tuple[XbrlModel, ImportGaps]:
   }
   gaps = ImportGaps(
     missing=[
-      "abstract flag on axes, domains and members",
       "a hypercube's name and primary items where its role presents no table",
       "an axis's default member, read as its domain",
       "concept references",
@@ -352,13 +351,19 @@ def _concepts(
     concepts[qname] = _bare(qname, namespaces, is_abstract=True, is_dimension_item=True)
     domain = obj.get("domainClass")
     if isinstance(domain, str) and domain and domain not in concepts:
-      concepts[domain] = _bare(domain, namespaces, is_domain_member=True)
+      concepts[domain] = _bare(
+        domain, namespaces, is_abstract=True, is_domain_member=True
+      )
 
+  # Domains and members are objects of their own in TAVI, not concepts, so no
+  # fact can report against one: abstract is what the model says they are.
   for key in ("domainClasses", "members"):
     for entry in _sequence(xbrl_model.get(key)):
       qname = str(_mapping(entry).get("name", ""))
       if qname and qname not in concepts:
-        concepts[qname] = _bare(qname, namespaces, is_domain_member=True)
+        concepts[qname] = _bare(
+          qname, namespaces, is_abstract=True, is_domain_member=True
+        )
 
   return concepts
 
@@ -829,6 +834,10 @@ def _facts(
 
     numeric_value = _float(value_str) if unit is not None else None
     decimals = value_obj.get("decimals")
+    if decimals is None and unit is not None and value_str is not None:
+      # Absent on a numeric fact means infinitely precise (the fact value
+      # object's `decimals`), which is how the emitter writes INF.
+      decimals = "INF"
     language = dimensions.get("xbrl:language")
     facts.append(
       XbrlFact(
diff --git a/xbrlkit/serve/session.py b/xbrlkit/serve/session.py
index 0f43816..532c1d9 100644
--- a/xbrlkit/serve/session.py
+++ b/xbrlkit/serve/session.py
@@ -259,14 +259,21 @@ def _enrich_filer(loaded: LoadedFiling, fields: Mapping[str, Any]) -> None:
 
 @dataclass
 class PublishedFiling:
-  """A filing as the public data CDN lists it: the holon to load, the document
-  as filed when it was published beside it, and the filer's ticker — the key
-  the catalog holds that filer's identity under."""
+  """A filing as the public data CDN lists it: the representations to load
+  (the TAVI model first, the holon beside it), the document as filed when it
+  was published too, and the filer's ticker — the key the catalog holds that
+  filer's identity under."""
 
   accession: str
-  holon_url: str
+  holon_url: str | None = None
   document_url: str | None = None
   ticker: str | None = None
+  tavi_url: str | None = None
+
+  @property
+  def model_urls(self) -> list[str]:
+    """The representations to try, in order: the TAVI model, then the holon."""
+    return [url for url in (self.tavi_url, self.holon_url) if url]
 
 
 def _published_from(
@@ -276,8 +283,8 @@ def _published_from(
   ticker: str | None = None,
 ) -> PublishedFiling | None:
   """The published filing a catalog entry or manifest describes, or ``None``
-  when it lists no holon."""
-  holon = document = None
+  when it lists neither a TAVI model nor a holon."""
+  holon = document = tavi = None
   for rep in representations if isinstance(representations, list) else []:
     if not isinstance(rep, dict):
       continue
@@ -288,15 +295,18 @@ def _published_from(
       continue
     if rep.get("kind") == "holon":
       holon = url
+    elif rep.get("kind") == "tavi":
+      tavi = url
     elif rep.get("kind") == "document":
       document = url
-  if not holon:
+  if not (holon or tavi):
     return None
   return PublishedFiling(
     accession=accession or "",
     holon_url=holon,
     document_url=document,
     ticker=ticker,
+    tavi_url=tavi,
   )
 
 
@@ -998,19 +1008,31 @@ def _filer_from_edgar(self, cik: str, client: Any = None) -> dict[str, Any]:
     }
 
   def _load_published(self, published: PublishedFiling, source: str) -> LoadedFiling:
-    """The filing from its published holon, with the document as filed beside
-    it when the CDN has that too — the same shape an EDGAR load gives, in a
-    fraction of the time and with no Arelle."""
-    into = self._tmp / (published.accession or Path(published.holon_url).stem)
-    holon = self._fetch(published.holon_url, into=into)
+    """The filing from its published TAVI model (or its holon when there is no
+    TAVI, or it cannot be read), with the document as filed beside it when the
+    CDN has that too — the same shape an EDGAR load gives, in a fraction of the
+    time and with no Arelle. The TAVI carries its text blocks inline, so there
+    are no fragments to fetch after it."""
+    urls = published.model_urls
+    into = self._tmp / (published.accession or Path(urls[0].split("?", 1)[0]).stem)
     document: Path | None = None
     if published.document_url:
       try:
         document = self._fetch(published.document_url, into=into)
       except requests.RequestException as exc:
         logger.warning("published document unavailable for %s: %s", source, exc)
-    logger.info("loading %s from its published holon", source)
-    loaded = self._load_json(holon, source, document=document)
+    loaded: LoadedFiling | None = None
+    for position, url in enumerate(urls):
+      try:
+        path = self._fetch(url, into=into)
+        logger.info("loading %s from %s", source, Path(url.split("?", 1)[0]).name)
+        loaded = self._load_json(path, source, document=document)
+        break
+      except (requests.RequestException, SourceError) as exc:
+        if position == len(urls) - 1:
+          raise
+        logger.warning("%s unavailable for %s (%s); trying the next", url, source, exc)
+    assert loaded is not None
     _enrich_filer(
       loaded, self._filer_metadata(loaded.model.entity.cik, ticker=published.ticker)
     )