Endpoint-resolved counts of graceful permutations of paths, n = 5 to 71

Exact counts G(n; a, b) of graceful permutations of the path P_n withfirst term a and last term b, for every n = 5..71 (all n^2 endpointpairs per n), together with the totals G(n) (OEIS A006967), the countingprograms, run logs and an independent checker. Contents- README.md: description, verification status, provenance.- graceful_counts_n5_71.tsv: G(n), n = 5..71, with verification status and run statistics.- graceful_endpoint_counts.csv: all endpoint tables in one file (header n,a,b,count; 121,806 rows). endpoints_per_n.zip: the same tables, one file per n.- source_code.zip: adam2_v3.cpp (layered dynamic programming after Adamaszek), graceful_enum.c and graceful_enum_shard.c (complete enumeration).- reproducibility_checks.zip: run outputs, verify_package.py and its log.- predictions_n51_64_67_71.md, predictions_addendum_n67_71.md: predictions recorded before computation. Verification- G(n) for n <= 59 agrees with the OEIS A006967 b-file, including an independent recomputation of a(41). For n = 60..71, G(n) rests on this implementation only (two builds or two thread counts agree).- Published value beyond the b-file: the single endpoint class G(64; 16, 48) = 1172380428523169632220649 agrees with Adamaszek (2006, Section 4). By a proved bijection it equals G(63; 16, 47), which the separately computed n = 63 table also reproduces. This is one alpha-labeling (extremal) class; it does not verify G(64) as a whole.- Endpoint tables for n <= 18 agree cell by cell with complete enumeration. Sums over the alpha-labeling classes agree with OEIS A395104 for N = 5..55.- Consistency with proved identities, all n <= 71: 4 | G(n); each table sums to G(n); exact identities G(2t+1; a, t-a) = G(2t; a, t-a) and G(2r+2; a, a+r+1) = G(2r+1; a, a+r) between separately computed n; the parity relation G(2r+2; a, a+r+1) = R(r+1, r-a) (mod 2); complementary classes even; classes violating the endpoint-parity condition are zero; zigzag class = 1. verify_package.py passes for all n = 5..71.- No independent implementation has yet confirmed G(n) or the endpoint tables for n = 60..71, apart from the single class above.- Predictions recorded before computation (odd endpoint classes and complementary classes for n = 51..64 and 67..71) were confirmed. The hashes were recorded in advance but not publicly timestamped. Licenses: data and documentation CC BY 4.0; source code MIT.The programs were written with AI assistance.