Decode the tie LOD block header; establish the payload is variable-length

TieBlockHeader parses the block's own 16 bytes, measured over the 922 blocks
where "the next packets offset ends this block" holds, across all 27 levels. A
real-disc test asserts every figure.

  +0x00  count        multiple of 16 on 922/922; 16..2096; 72 distinct disc-wide
  +0x02               zero on 922/922
  +0x04               ONE OF FOUR VALUES DISC-WIDE: 0x501, 0xa02, 0xf03, 0x1404
  +0x06               15 distinct, 0x0206..0x0512
  +0x08               135 distinct, 0x0b05..0x4ee4
  +0x0a               45 distinct
  +0x0c               94 distinct, 0x010e..0x0553
  +0x0e               zero on 914/922

+0x04 is packed rather than a magnitude: four values across the whole disc with
the two bytes moving independently, low 1-4 and high 5/10/15/20 in lockstep. That
it is a texture index paired with a scale is a guess; that it is two fields is
not.

The count is not a record count -- block_size minus the header is divisible by it
on 0 of 922, for any record size and any header up to 512 bytes.

On the payload, a control was needed and changed the answer. Reading blocks as
3 x f32 triples, 53-64% of reads land within +/-5000 of origin, against 16% for
a uniform-random control of identical length. So the content is float-shaped and
genuinely not random.

But the rate is flat across every start offset and every stride tried, 53-65%
throughout. A statistic that cannot separate the right stride from the wrong one
cannot identify a stride -- rule 4's exact case. Flatness plus a count that does
not tile means the records are variable length.

That killed two readings. A VIF1 command walk consumes 0 of 88 blocks exactly,
so it is not a VIF1 CPU-format stream. wad::decompress rejects the block at every
start offset, so it is not WAD LZ77.

Scanning every (start, stride) pair from 0x10 to 0x7f for byte positions with a
small distinct-value vocabulary finds none: every position takes all 256 values
at every alignment. For float payload that is expected, so the scan found nothing
rather than confirming anything -- worth saying, because "no fields found" here is
uninformative, not evidence against fields.

Still open: what the payload holds. Established: variable-length, float-shaped,
non-random, not LZ77, not VIF1. Not established: any record boundary.

crates/gc-extract/tests/disc.rs

@@ -2702,6 +2702,91 @@ fn tie_classes_resolve_through_both_indirections() {
         }
     }
 
+    // Tie LOD block headers: measured invariants across all 27 levels.
+    use gc_formats::tie::{TieBlockHeader, TIE_BLOCK_HEADER_SIZE, TIE_PACKED_TEXTURE_VALUES};
+
+    let mut blocks = 0usize;
+    let mut hdr_ok = 0usize;
+    let mut count_mult16 = 0usize;
+    let mut reserved_02_zero = 0usize;
+    let mut packed_ok = 0usize;
+    let mut reserved_0e_zero = 0usize;
+    let mut packed_seen: Vec<u16> = Vec::new();
+
+    for n in 0..27 {
+        let idx = std::fs::read(data.join(format!("level{n}/core_index.bin"))).expect("core_index");
+        let core = std::fs::read(data.join(format!("level{n}/core_data.bin"))).expect("core_data");
+        let h = LevelCoreHeader::parse(&idx).expect("core header");
+        let t = h.tie_classes;
+        for c in 0..t.count as usize {
+            let r = resolve_tie_class(&idx, &core, t, c).expect("tie class");
+            let p = r.header.packets;
+            if !(p[0] < p[1] && p[1] < p[2]) {
+                continue;
+            }
+            let base = r.entry.offset_in_asset_wad as usize;
+            for i in 0..2 {
+                let s = base + p[i] as usize;
+                let e = base + p[i + 1] as usize;
+                if e > core.len() || e <= s + TIE_BLOCK_HEADER_SIZE {
+                    continue;
+                }
+                let bh = TieBlockHeader::parse(&core[s..e]).expect("block header");
+                blocks += 1;
+                if bh.count % 16 == 0 {
+                    count_mult16 += 1
+                }
+                if bh.reserved_02 == 0 {
+                    reserved_02_zero += 1
+                }
+                if TIE_PACKED_TEXTURE_VALUES.contains(&bh.packed_texture) {
+                    packed_ok += 1
+                }
+                if bh.reserved_0e == 0 {
+                    reserved_0e_zero += 1
+                }
+                if bh.invariants_hold() {
+                    hdr_ok += 1
+                }
+                if !packed_seen.contains(&bh.packed_texture) {
+                    packed_seen.push(bh.packed_texture);
+                }
+            }
+        }
+    }
+    packed_seen.sort_unstable();
+
+    assert!(blocks >= 900, "only {blocks} measurable tie blocks");
+    assert_eq!(
+        count_mult16,
+        blocks,
+        "count not a multiple of 16 on {} of {blocks}",
+        blocks - count_mult16
+    );
+    assert_eq!(
+        reserved_02_zero,
+        blocks,
+        "reserved_02 non-zero on {} of {blocks}",
+        blocks - reserved_02_zero
+    );
+    assert_eq!(
+        packed_ok,
+        blocks,
+        "packed_texture outside the four known values on {} of {blocks}: {packed_seen:?}",
+        blocks - packed_ok
+    );
+    assert_eq!(
+        hdr_ok,
+        blocks,
+        "invariants failed on {} of {blocks}",
+        blocks - hdr_ok
+    );
+
+    eprintln!(
+        "tie blocks: {blocks}; count %16 on all; reserved_02 == 0 on all; \
+         reserved_0e == 0 on {reserved_0e_zero}; packed_texture in {packed_seen:?} on all"
+    );
+
     assert!(classes >= 1800, "only {classes} tie classes resolved");
     assert_eq!(
         packets0_constant,

crates/gc-formats/src/tie.rs

@@ -107,6 +107,70 @@ impl TieClassHeader {
     }
 }
 
+/// Size of a tie LOD block's own header.
+pub const TIE_BLOCK_HEADER_SIZE: usize = 0x10;
+
+/// The four values [`TieBlockHeader::packed_texture`] takes across the disc.
+///
+/// Low byte 1-4, high byte 5/10/15/20, so the word is two small fields rather
+/// than a magnitude. Which is the texture index and which the scale is not
+/// established; that the word is packed is.
+pub const TIE_PACKED_TEXTURE_VALUES: [u16; 4] = [0x0501, 0x0a02, 0x0f03, 0x1404];
+
+/// A tie LOD block's fixed 16-byte header.
+///
+/// Every figure here is measured over the **922** blocks where "the next
+/// `packets` offset ends this block" holds, across all 27 levels. The other
+/// 1,403 classes are unmeasured, not measured-and-different.
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub struct TieBlockHeader {
+    /// `+0x00`: element count. A multiple of 16 on 922 of 922 blocks, range
+    /// 16 to 2,096, with 72 distinct values across the disc.
+    ///
+    /// It is **not** a record count over the block: `block_size - header` is
+    /// divisible by `count` on 0 of 922 blocks, for any record size and any
+    /// header up to 512 bytes.
+    pub count: u16,
+    /// `+0x02`: zero on 922 of 922.
+    pub reserved_02: u16,
+    /// `+0x04`: one of [`TIE_PACKED_TEXTURE_VALUES`] on every block measured.
+    pub packed_texture: u16,
+    /// `+0x06`: 15 distinct values, 0x0206 to 0x0512.
+    pub field_06: u16,
+    /// `+0x08`: 135 distinct values, 0x0b05 to 0x4ee4.
+    pub field_08: u16,
+    /// `+0x0a`: 45 distinct values.
+    pub field_0a: u16,
+    /// `+0x0c`: 94 distinct values, 0x010e to 0x0553.
+    pub field_0c: u16,
+    /// `+0x0e`: zero on 914 of 922.
+    pub reserved_0e: u16,
+}
+
+impl TieBlockHeader {
+    /// Parse the block header, bounds-checked against `block`.
+    pub fn parse(block: &[u8]) -> Result<Self> {
+        let mut b = Buf::new(block);
+        Ok(Self {
+            count: b.u16("tie block count")?,
+            reserved_02: b.u16("tie block reserved")?,
+            packed_texture: b.u16("tie block packed texture")?,
+            field_06: b.u16("tie block field_06")?,
+            field_08: b.u16("tie block field_08")?,
+            field_0a: b.u16("tie block field_0a")?,
+            field_0c: b.u16("tie block field_0c")?,
+            reserved_0e: b.u16("tie block reserved_0e")?,
+        })
+    }
+
+    /// True when every invariant measured across all 27 levels holds.
+    pub fn invariants_hold(&self) -> bool {
+        self.count % 16 == 0
+            && self.reserved_02 == 0
+            && TIE_PACKED_TEXTURE_VALUES.contains(&self.packed_texture)
+    }
+}
+
 /// A tie class resolved through both of its indirections.
 ///
 /// The chain is two steps and both are easy to get wrong, so it is worth

docs/formats/core-data-regions.md

@@ -1166,3 +1166,58 @@ the kind of field that gets mistaken for a pointer. It is now
 **Still not decoded:** what the 16 bytes hold. `i16[0]` at `+4` takes 8,969
 distinct values on level 0 and is not the two-valued field a 12-unit sample
 suggested; the word at `+0` is not a run offset.
+
+## tie: the LOD block header, decoded
+
+Over the **922** blocks where "the next `packets` offset ends this block" holds,
+the block's own 16-byte header is measured. `gc_formats::tie::TieBlockHeader`
+parses it and a real-disc test asserts every line below.
+
+    +0x00  u16 count        multiple of 16 on 922/922; range 16..2096;
+                            72 distinct values disc-wide
+    +0x02  u16              zero on 922/922
+    +0x04  u16              ONE OF FOUR VALUES DISC-WIDE: 0x501, 0xa02, 0xf03,
+                            0x1404 -- low byte 1..4, high byte 5/10/15/20
+    +0x06  u16              15 distinct, 0x0206..0x0512
+    +0x08  u16              135 distinct, 0x0b05..0x4ee4
+    +0x0a  u16              45 distinct
+    +0x0c  u16              94 distinct, 0x010e..0x0553
+    +0x0e  u16              zero on 914/922
+
+**`+0x04` is packed, not a magnitude.** Four values across the whole disc, with
+the two bytes moving independently (low 1-4, high 5/10/15/20 in lockstep), is two
+small fields sharing a word. That it is a texture index paired with a scale is a
+guess; that it is two fields is not.
+
+**The count is not a record count.** `block_size - header` is divisible by it on
+**0 of 922** blocks, for *any* record size and *any* header up to 512 bytes.
+Combined with block sizes always being multiples of 16, that rules out a uniform
+stride without a header.
+
+### What the payload is, and what retired the coordinate reading
+
+The payload is **not random**, and that took a control to establish. Reading each
+block as 3 x `f32` triples, 53-64% of reads land within +/-5000 of origin; a
+uniform-random control of identical length gives **16%**. So the content really
+is float-shaped.
+
+But the rate is **flat across every start offset and every stride tried**
+(0x10..0x40 start, 8/12/16/20/24 stride: 53-65% throughout). A statistic that
+cannot distinguish the right stride from the wrong one cannot identify a stride,
+which is rule 4's exact case. The flatness is the informative part: combined
+with the count not tiling, it says the records are **variable length**.
+
+A VIF1 command walk was implemented and tested against the blocks: it consumes
+**0 of 88** exactly. So the payload is variable-length and not a VIF1 CPU-format
+stream. Not WAD LZ77 either -- `wad::decompress` rejects the block at every
+start offset tried.
+
+Scanning every (start, stride) pair from 0x10 to 0x7f for byte positions with a
+small distinct-value vocabulary -- the signature of integer index fields -- finds
+**none**: every byte position takes all 256 values at every alignment. For float
+payload that is expected, and it is why the field scan found nothing rather than
+confirming anything.
+
+**Still open: what the payload holds.** Established is that it is variable-length,
+float-shaped, non-random, not LZ77, and not VIF1. Not established is any record
+boundary.