{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EXH6VHTRDQBH6O2ZE2GXYSZSNY","short_pith_number":"pith:EXH6VHTR","canonical_record":{"source":{"id":"1609.03811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-09-13T13:01:39Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"de2b9f0c0d703b6611c01fa2e3ca5f23d424c2854f959ee3af8390f5fcebcfb5","abstract_canon_sha256":"55571a6afc5e8fe4581d5d799dcef886bb89aafcb091be0b722c43ad20e89456"},"schema_version":"1.0"},"canonical_sha256":"25cfea9e711c027f3b59268d7c4b326e1b41795e08ca2844f90ea7984baa53dd","source":{"kind":"arxiv","id":"1609.03811","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03811","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03811v1","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03811","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"EXH6VHTRDQBH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXH6VHTRDQBH6O2Z","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXH6VHTR","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EXH6VHTRDQBH6O2ZE2GXYSZSNY","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-09-13T13:01:39Z","cross_cats_sorted":["cond-mat.other"],"title_canon_sha256":"de2b9f0c0d703b6611c01fa2e3ca5f23d424c2854f959ee3af8390f5fcebcfb5","abstract_canon_sha256":"55571a6afc5e8fe4581d5d799dcef886bb89aafcb091be0b722c43ad20e89456"},"schema_version":"1.0"},"canonical_sha256":"25cfea9e711c027f3b59268d7c4b326e1b41795e08ca2844f90ea7984baa53dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:42.359010Z","signature_b64":"7toThbaDAA78Qt+HX2E21KZ1PNGRI7rAGv+7//hph/Fap4DobShD+xUOTP47Zwps+xyDu8aLKPTvrbrOPNFXCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25cfea9e711c027f3b59268d7c4b326e1b41795e08ca2844f90ea7984baa53dd","last_reissued_at":"2026-05-18T01:04:42.358563Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:42.358563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03811","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sUgEKcAA4+lKHOlXyfy/QK/hz0pjurq2jpDXc928mz02/Z4lQNTN24iVtjv/ObGMS5qnFxQVk+8CWsj3jbDUBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:23:46.940909Z"},"content_sha256":"e3781fecd39a3eeb4436b52fdd3fcd92c2cd07293c769fd46d33b9253e1bd901","schema_version":"1.0","event_id":"sha256:e3781fecd39a3eeb4436b52fdd3fcd92c2cd07293c769fd46d33b9253e1bd901"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EXH6VHTRDQBH6O2ZE2GXYSZSNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cutting self-similar space-filling sphere packings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other"],"primary_cat":"cond-mat.soft","authors_text":"D. V. St\\\"ager, H. J. Herrmann","submitted_at":"2016-09-13T13:01:39Z","abstract_excerpt":"Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we prove that cutting along a random hyperplane leads in general to a packing with a fractal dimension of the one of the uncut packing minus one. Second, we find special cuts which can be constructed themselves by inversive geometry. Such special cuts have specific fractal dimensions, which we demonstrate by cutting a three- and a four-dimensional packing. The "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03811","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SyY/QA/1EJ1d27asBsemZ0dqKOZzECROpeJK/wt6l3VZyn65vOj6G+zMfyrvaCevzEFYNAEwEfUtWzCm0hG9Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:23:46.941259Z"},"content_sha256":"bc99ad61e832d3583bceb476bfd00d7b30f835298ba1adbb97f9a6688ec8bc4e","schema_version":"1.0","event_id":"sha256:bc99ad61e832d3583bceb476bfd00d7b30f835298ba1adbb97f9a6688ec8bc4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/bundle.json","state_url":"https://pith.science/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/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":"2026-06-25T08:23:46Z","links":{"resolver":"https://pith.science/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY","bundle":"https://pith.science/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/bundle.json","state":"https://pith.science/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXH6VHTRDQBH6O2ZE2GXYSZSNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EXH6VHTRDQBH6O2ZE2GXYSZSNY","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":"55571a6afc5e8fe4581d5d799dcef886bb89aafcb091be0b722c43ad20e89456","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-09-13T13:01:39Z","title_canon_sha256":"de2b9f0c0d703b6611c01fa2e3ca5f23d424c2854f959ee3af8390f5fcebcfb5"},"schema_version":"1.0","source":{"id":"1609.03811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03811","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03811v1","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03811","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"EXH6VHTRDQBH","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"EXH6VHTRDQBH6O2Z","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"EXH6VHTR","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:bc99ad61e832d3583bceb476bfd00d7b30f835298ba1adbb97f9a6688ec8bc4e","target":"graph","created_at":"2026-05-18T01:04:42Z","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":"Any space-filling packing of spheres can be cut by a plane to obtain a space-filling packing of disks. Here, we deal with space-filling packings generated using inversive geometry leading to exactly self-similar fractal packings. First, we prove that cutting along a random hyperplane leads in general to a packing with a fractal dimension of the one of the uncut packing minus one. Second, we find special cuts which can be constructed themselves by inversive geometry. Such special cuts have specific fractal dimensions, which we demonstrate by cutting a three- and a four-dimensional packing. The ","authors_text":"D. V. St\\\"ager, H. J. Herrmann","cross_cats":["cond-mat.other"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-09-13T13:01:39Z","title":"Cutting self-similar space-filling sphere packings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03811","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:e3781fecd39a3eeb4436b52fdd3fcd92c2cd07293c769fd46d33b9253e1bd901","target":"record","created_at":"2026-05-18T01:04:42Z","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":"55571a6afc5e8fe4581d5d799dcef886bb89aafcb091be0b722c43ad20e89456","cross_cats_sorted":["cond-mat.other"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2016-09-13T13:01:39Z","title_canon_sha256":"de2b9f0c0d703b6611c01fa2e3ca5f23d424c2854f959ee3af8390f5fcebcfb5"},"schema_version":"1.0","source":{"id":"1609.03811","kind":"arxiv","version":1}},"canonical_sha256":"25cfea9e711c027f3b59268d7c4b326e1b41795e08ca2844f90ea7984baa53dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25cfea9e711c027f3b59268d7c4b326e1b41795e08ca2844f90ea7984baa53dd","first_computed_at":"2026-05-18T01:04:42.358563Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:42.358563Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7toThbaDAA78Qt+HX2E21KZ1PNGRI7rAGv+7//hph/Fap4DobShD+xUOTP47Zwps+xyDu8aLKPTvrbrOPNFXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:42.359010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3781fecd39a3eeb4436b52fdd3fcd92c2cd07293c769fd46d33b9253e1bd901","sha256:bc99ad61e832d3583bceb476bfd00d7b30f835298ba1adbb97f9a6688ec8bc4e"],"state_sha256":"d3f281af04021f8cf3f49d4fd2dff60eff3ff72476109e02c4df741c8dc41f79"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"re2vzhCyQR2x23hdStmEFpaLTbcxtbX7+d0HQz5InM2P//KowntgawSOkwlJwaZVR3K23NaAvKOIr53dDVVvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:23:46.943296Z","bundle_sha256":"13050b228cdd0bee92ed57503185ebe4cace4ce8bc6187620c2dff10a03e8d2a"}}