{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4B3HJPDJWLIUX33OZASAMMOIGN","short_pith_number":"pith:4B3HJPDJ","canonical_record":{"source":{"id":"2606.07456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-05T17:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"aaad603ea112742e3816423ea627aa7d23336017f9aca1551814b1bb32d6f30e","abstract_canon_sha256":"21e9c0476907e94db3d3a1d000991ee51bb8d790f5b7007fb27c3f4f7f15bbd1"},"schema_version":"1.0"},"canonical_sha256":"e07674bc69b2d14bef6ec8240631c833433c80c3d47614cb7c0190a3e2985685","source":{"kind":"arxiv","id":"2606.07456","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07456","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07456v1","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07456","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"4B3HJPDJWLIU","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"4B3HJPDJWLIUX33O","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"4B3HJPDJ","created_at":"2026-06-08T01:05:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4B3HJPDJWLIUX33OZASAMMOIGN","target":"record","payload":{"canonical_record":{"source":{"id":"2606.07456","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-05T17:03:34Z","cross_cats_sorted":[],"title_canon_sha256":"aaad603ea112742e3816423ea627aa7d23336017f9aca1551814b1bb32d6f30e","abstract_canon_sha256":"21e9c0476907e94db3d3a1d000991ee51bb8d790f5b7007fb27c3f4f7f15bbd1"},"schema_version":"1.0"},"canonical_sha256":"e07674bc69b2d14bef6ec8240631c833433c80c3d47614cb7c0190a3e2985685","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-08T01:05:28.140081Z","signature_b64":"rTktwZ2ewX0Vl8XuR+0EDOqzzeiqV4Wk6gnLfkVwSeWM5e02t0UOVyazVNXnhTH7irV0yR1AM1dQzCDHZzN8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e07674bc69b2d14bef6ec8240631c833433c80c3d47614cb7c0190a3e2985685","last_reissued_at":"2026-06-08T01:05:28.139120Z","signature_status":"signed_v1","first_computed_at":"2026-06-08T01:05:28.139120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.07456","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-08T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RB4mXes0UDwkCNZguDZ4KCvMD9OeBePi0xNRsL6DWHY0XLgzv889g9Xr0GZjgj71O5a1tEGKyehJXoYTsli+Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:13:51.193101Z"},"content_sha256":"82f2348de45e5058fd69d3c42356c37ff54d4a30dd94a9d822dbf0e602568a97","schema_version":"1.0","event_id":"sha256:82f2348de45e5058fd69d3c42356c37ff54d4a30dd94a9d822dbf0e602568a97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4B3HJPDJWLIUX33OZASAMMOIGN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A study of maximal shifts in the minimal graded free resolution of the residue field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adela Vraciu, Dinesh Limbu, Liana M. \\c{S}ega","submitted_at":"2026-06-05T17:03:34Z","abstract_excerpt":"We study two invariants, rate and slant, that describe the extremal behavior of the maximal shifts in the minimal free resolution of the residue field over a standard graded algebra. We provide bounds and computations of these invariants for a variety of rings, including compressed level algebras, rings defined by general forms and rings defined by monomials. We also prove an asymptotic additivity property of the maximal shifts for certain classes of rings, including Golod rings, which allows to interpret slant as a limit."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07456","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.07456/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-08T01:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz6Q046tUhAs9KZnNa9c/ThKoRZexiegaZS9OtVkSEcV9RJerKR0p7Yb9mbc5PKdI3PEJBHkNg7jo82AUdq6BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:13:51.193711Z"},"content_sha256":"11eba7793863d3a1ac955a2af07288d5a1d855e81a7e86ee0f37b5c622d79829","schema_version":"1.0","event_id":"sha256:11eba7793863d3a1ac955a2af07288d5a1d855e81a7e86ee0f37b5c622d79829"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4B3HJPDJWLIUX33OZASAMMOIGN/bundle.json","state_url":"https://pith.science/pith/4B3HJPDJWLIUX33OZASAMMOIGN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4B3HJPDJWLIUX33OZASAMMOIGN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T19:13:51Z","links":{"resolver":"https://pith.science/pith/4B3HJPDJWLIUX33OZASAMMOIGN","bundle":"https://pith.science/pith/4B3HJPDJWLIUX33OZASAMMOIGN/bundle.json","state":"https://pith.science/pith/4B3HJPDJWLIUX33OZASAMMOIGN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4B3HJPDJWLIUX33OZASAMMOIGN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4B3HJPDJWLIUX33OZASAMMOIGN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"21e9c0476907e94db3d3a1d000991ee51bb8d790f5b7007fb27c3f4f7f15bbd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-05T17:03:34Z","title_canon_sha256":"aaad603ea112742e3816423ea627aa7d23336017f9aca1551814b1bb32d6f30e"},"schema_version":"1.0","source":{"id":"2606.07456","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.07456","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.07456v1","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.07456","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"4B3HJPDJWLIU","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_16","alias_value":"4B3HJPDJWLIUX33O","created_at":"2026-06-08T01:05:28Z"},{"alias_kind":"pith_short_8","alias_value":"4B3HJPDJ","created_at":"2026-06-08T01:05:28Z"}],"graph_snapshots":[{"event_id":"sha256:11eba7793863d3a1ac955a2af07288d5a1d855e81a7e86ee0f37b5c622d79829","target":"graph","created_at":"2026-06-08T01:05:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.07456/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study two invariants, rate and slant, that describe the extremal behavior of the maximal shifts in the minimal free resolution of the residue field over a standard graded algebra. We provide bounds and computations of these invariants for a variety of rings, including compressed level algebras, rings defined by general forms and rings defined by monomials. We also prove an asymptotic additivity property of the maximal shifts for certain classes of rings, including Golod rings, which allows to interpret slant as a limit.","authors_text":"Adela Vraciu, Dinesh Limbu, Liana M. \\c{S}ega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-05T17:03:34Z","title":"A study of maximal shifts in the minimal graded free resolution of the residue field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.07456","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:82f2348de45e5058fd69d3c42356c37ff54d4a30dd94a9d822dbf0e602568a97","target":"record","created_at":"2026-06-08T01:05:28Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"21e9c0476907e94db3d3a1d000991ee51bb8d790f5b7007fb27c3f4f7f15bbd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2026-06-05T17:03:34Z","title_canon_sha256":"aaad603ea112742e3816423ea627aa7d23336017f9aca1551814b1bb32d6f30e"},"schema_version":"1.0","source":{"id":"2606.07456","kind":"arxiv","version":1}},"canonical_sha256":"e07674bc69b2d14bef6ec8240631c833433c80c3d47614cb7c0190a3e2985685","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e07674bc69b2d14bef6ec8240631c833433c80c3d47614cb7c0190a3e2985685","first_computed_at":"2026-06-08T01:05:28.139120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-08T01:05:28.139120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rTktwZ2ewX0Vl8XuR+0EDOqzzeiqV4Wk6gnLfkVwSeWM5e02t0UOVyazVNXnhTH7irV0yR1AM1dQzCDHZzN8Dg==","signature_status":"signed_v1","signed_at":"2026-06-08T01:05:28.140081Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.07456","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82f2348de45e5058fd69d3c42356c37ff54d4a30dd94a9d822dbf0e602568a97","sha256:11eba7793863d3a1ac955a2af07288d5a1d855e81a7e86ee0f37b5c622d79829"],"state_sha256":"e0013eae293f7eb2c226c3a637bbd7219023b5dc7c3555c56aba523bd7cebcba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nc4mP0QapaXMV6lj5rML9k8evVNnX1DDQx+K4wtJZPdQbtsEhbIsztEA7w5oLBCDzpxGBnnN2u37/d7idkBkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:13:51.196412Z","bundle_sha256":"7424b9551ecce8efc8deb28ba48897a89f28199842a1716d3a0b342f4db47de6"}}