{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SKYVRZ4MLDMTAYIMOEDKHRXBEQ","short_pith_number":"pith:SKYVRZ4M","canonical_record":{"source":{"id":"1504.05548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T19:01:01Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"84f63b0617a7e530d99b8f1925ddf8e7ba077b415d03edb13e481228dce6a988","abstract_canon_sha256":"f8a531c3e5c450d93aa1f6326246d643f47f1e6ea70717c5dd496b8545ff2fc0"},"schema_version":"1.0"},"canonical_sha256":"92b158e78c58d930610c7106a3c6e1241794c527605b47b725279d4a0a585d98","source":{"kind":"arxiv","id":"1504.05548","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05548","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05548v1","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05548","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"SKYVRZ4MLDMT","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SKYVRZ4MLDMTAYIM","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SKYVRZ4M","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SKYVRZ4MLDMTAYIMOEDKHRXBEQ","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T19:01:01Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"84f63b0617a7e530d99b8f1925ddf8e7ba077b415d03edb13e481228dce6a988","abstract_canon_sha256":"f8a531c3e5c450d93aa1f6326246d643f47f1e6ea70717c5dd496b8545ff2fc0"},"schema_version":"1.0"},"canonical_sha256":"92b158e78c58d930610c7106a3c6e1241794c527605b47b725279d4a0a585d98","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:25.790325Z","signature_b64":"d9YV4MVgyIXLLyLj2UcNLf4tGuUxgzzigmX6iVurvg2cAKyZNXCw48Im0Orhcxn5957qFL43SdMabbOFuVZZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92b158e78c58d930610c7106a3c6e1241794c527605b47b725279d4a0a585d98","last_reissued_at":"2026-05-18T01:17:25.789727Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:25.789727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05548","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":"2026-05-18T01:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6ySLkPBBjuZEABk/pD+CrpP2syFRTBf9T4hzA3SXJbdJsHtZXFzFq6O5P5m0UE+GdZ+3ExLuOQ52vWl3lKFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:14:10.180701Z"},"content_sha256":"824c541ffec1032993e4371345dbc408a41f86a46cce0b65af271a3b3870b840","schema_version":"1.0","event_id":"sha256:824c541ffec1032993e4371345dbc408a41f86a46cce0b65af271a3b3870b840"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SKYVRZ4MLDMTAYIMOEDKHRXBEQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symbolic powers of planar point configurations II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Halszka Tutaj-Gasinska, Marcin Dumnicki, Tomasz Szemberg","submitted_at":"2015-04-21T19:01:01Z","abstract_excerpt":"We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and we extend our considerations to the asymptotic setting of Waldschmidt constants. We introduce the concept of Bezout Decomposition which might be of independent interest."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05548","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":""},"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":"2026-05-18T01:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1DjQ87QdeXOv8j2Uptm8a9ltBpbFaTp6NIPvATykbCbPKb9nlM9V6wKyCo/FMogrmc40ocO6BF8H+xGMfPDBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:14:10.181049Z"},"content_sha256":"9feaf9a672c1ebc542452d66ee4c0e2f6ad63291681f12666271415aa2952211","schema_version":"1.0","event_id":"sha256:9feaf9a672c1ebc542452d66ee4c0e2f6ad63291681f12666271415aa2952211"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/bundle.json","state_url":"https://pith.science/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/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":"2026-06-04T17:14:10Z","links":{"resolver":"https://pith.science/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ","bundle":"https://pith.science/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/bundle.json","state":"https://pith.science/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SKYVRZ4MLDMTAYIMOEDKHRXBEQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SKYVRZ4MLDMTAYIMOEDKHRXBEQ","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":"f8a531c3e5c450d93aa1f6326246d643f47f1e6ea70717c5dd496b8545ff2fc0","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T19:01:01Z","title_canon_sha256":"84f63b0617a7e530d99b8f1925ddf8e7ba077b415d03edb13e481228dce6a988"},"schema_version":"1.0","source":{"id":"1504.05548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05548","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05548v1","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05548","created_at":"2026-05-18T01:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"SKYVRZ4MLDMT","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SKYVRZ4MLDMTAYIM","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SKYVRZ4M","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:9feaf9a672c1ebc542452d66ee4c0e2f6ad63291681f12666271415aa2952211","target":"graph","created_at":"2026-05-18T01:17:25Z","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"},"paper":{"abstract_excerpt":"We study initial sequences of various configurations of planar points. We answer several questions asked in our previous paper (Symbolic powers of planar point configurations), and we extend our considerations to the asymptotic setting of Waldschmidt constants. We introduce the concept of Bezout Decomposition which might be of independent interest.","authors_text":"Halszka Tutaj-Gasinska, Marcin Dumnicki, Tomasz Szemberg","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T19:01:01Z","title":"Symbolic powers of planar point configurations II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05548","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":"sha256:824c541ffec1032993e4371345dbc408a41f86a46cce0b65af271a3b3870b840","target":"record","created_at":"2026-05-18T01:17:25Z","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":"f8a531c3e5c450d93aa1f6326246d643f47f1e6ea70717c5dd496b8545ff2fc0","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-04-21T19:01:01Z","title_canon_sha256":"84f63b0617a7e530d99b8f1925ddf8e7ba077b415d03edb13e481228dce6a988"},"schema_version":"1.0","source":{"id":"1504.05548","kind":"arxiv","version":1}},"canonical_sha256":"92b158e78c58d930610c7106a3c6e1241794c527605b47b725279d4a0a585d98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92b158e78c58d930610c7106a3c6e1241794c527605b47b725279d4a0a585d98","first_computed_at":"2026-05-18T01:17:25.789727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:25.789727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d9YV4MVgyIXLLyLj2UcNLf4tGuUxgzzigmX6iVurvg2cAKyZNXCw48Im0Orhcxn5957qFL43SdMabbOFuVZZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:25.790325Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:824c541ffec1032993e4371345dbc408a41f86a46cce0b65af271a3b3870b840","sha256:9feaf9a672c1ebc542452d66ee4c0e2f6ad63291681f12666271415aa2952211"],"state_sha256":"6e198da9504a806010e49cf02e15bbe5ddc5f0bcf12acf79580161cdce019e7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K1o4IONNJE2BF5GvGO1wXZP/Awi1IZBIeLqtToMdxb8uHmBtVMKXLD672ISARe95NzWshTd3fwyQbvZMxM5qBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:14:10.183615Z","bundle_sha256":"017c3d2d1cab74658a19475d3154ee97a206fd3078d0a384bd3ad90eb27eb393"}}